IMUCET 2026 MARATHON PHYSICS ♾️| SURESHOT QUESTIONS🔥| Marine Edge

Indexed: 2026-05-21

[00:00:01]Hello students, welcome to Marine Edge.

[00:00:03]Uh this is your physics tutor, Aditi Singh. Today we'll be discussing a guess paper that we have prepared from our end for the upcoming IMUCET for physics.

[00:00:11]In [snorts] our previous lecture, we also covered all the chapters with the help of mind maps of physics. So, in case if you want to get a quick revision, you can check on that. So, continuing on, let's get started with the physics.

[00:00:24]So, the first question.

[00:00:27]Um let me take a minute. Okay. All right.

[00:00:31]Now, the height at which the value of acceleration due to gravity becomes 25% of its value at the surface of Earth's radius. Now, we know that the formula for acceleration due to gravity g' is equals to g r divided by r + h. Let's say h is the height at which the acceleration due to gravity will become 25%. This is the formula. So, now as we can see that the final gravity is 1 by 4. So, if we just take uh this g here, so the g' by g that is equal to 1 by 4 is equals to r squared by r + h.

[00:01:07]Correct? Now, uh the whole square.

[00:01:09]Sorry.

[00:01:14]Uh let's write it like this.

[00:01:17]r squared by r + h, right?

[00:01:21]So, uh we can write it as 1 by 2 equals r upon r + h.

[00:01:27]So, that gives us what?

[00:01:28]2r equals r + h.

[00:01:32]So, that gives us r is equals to h, right?

[00:01:35]So, at height r at height h is equals to r, the gravitational field will become 25% of what it is initially at the surface of Earth, right?

[00:01:45]Now, moving forward. A body of mass 2 kg moving with the velocity of 10 m collides in a head-on collision with another body of mass 2 kg at rest. Now, as we can see both masses m1 and m2 are equal, right? That is 2 kg. And it is a perfectly elastic collision. So, there is no loss of kinetic energy. So, whatever initial energy was in the body uh first body, that will get completely transferred to the second body. So, after the collision, the velocity of the first body will become zero. And the velocity of second body will become 10, okay? Now, next. Escape velocity from Earth's surface is 11.2 km/s. For escape velocity from a planet whose mass and radius are both twice that of Earth, will be So, we know that the formula for escape velocity VE is equals to under root 2 GM upon R, where R is the radius of whichever planet we're talking about.

[00:02:37]Now, if mass also becomes So, for this uh secondary planet, the escape velocity will be equal to under root 2 into mass will be also become twice, and the radius of radius of the planet is also becoming twice. So, in the end, we are receiving the same value. So, the final answer will be again same as initial value, that is uh that will be the escape velocity from of Earth only, that is 11.2 km/s, right?

[00:03:00]Now, next.

[00:03:02]A force F is equal uh 3 I cap plus 4 J cap plus 5 K cap.

[00:03:08]Oh, sorry, minus 5 K cap.

[00:03:13]Uh acts on a body. It is asking for the magnitude of the force. So, basically, it is a vector question. It is asking for the magnitude of the vector. So, what is the formula? The formula is we just square all those three values and take the under root of it. So, 3 squared plus 4 squared plus 5 squared.

[00:03:30]That will give us what? Under root 9 plus 16 plus 25.

[00:03:35]That is 5 root 2.

[00:03:37]Now, suppose the question would have asked you about the unit vector. So, you could have just divided this uh vector by 5.2 to give the unit vector, right?

[00:03:47]Now, moving forward, a ball is thrown vertically upward with a velocity of 20 m/s. So, initial velocity is 20. The maximum height reached it. So, see initial velocity is 20. At maximum height, the velocity of ball will be zero, right? So, V is zero.

[00:04:02]And so, S is equals to Sorry, V squared is equals to U squared plus 2 AS, right? And A or the acceleration in this case will be gravity acting in opposite direction, right? Gravity is acting in downward direction. So, for that, zero is equals to 20 squared plus 2 into minus 10 let's take for gravity Oh, yeah, it's given already here. If it is not given in the question, uh you can take 9.8 as well as 10, whichever suits the answer, okay?

[00:04:33]And if both answers are also available, in that case, always ensure taking 9.8.

[00:04:38]And S. So, what do we get? 400 is equals to 2 into 10.

[00:04:45]That gives us maximum height as 20.

[00:04:47]Right? Next.

[00:04:49]Now, moment of inertia of a solid sphere mass M and radius R about its diameter. What is the formula for moment of inertia? 2 MR squared upon five, right? About its diameter.

[00:05:01]So, these are some of the formulas that you will be you must be remembering in your exam, right?

[00:05:06]Now, a wheel of mass 10 kg has a moment of inertia of 160 kg m m squared about its own axis. What is the radius of gyration? So, what is the formula for radius of gyration?

[00:05:17]Uh the the radius of uh let's say Okay, this is not working. Great.

[00:05:23]So, the formula for radius of gyration K is equals to under root I upon M, correct? So, value of I is given to us 160. Mass is also given to us 10. We cancel it out, you'll get your answer as 4 m, correct?

[00:05:36]Now, a particle performing uniform circular motion has an angular momentum L. So, angular momentum is given to us as L.

[00:05:43]Its angular frequency is doubled and kinetic energy is halved.

[00:05:47]So, uh omega is doubled.

[00:05:50]Omega becomes 2 omega and kinetic energy becomes 1 by 2. So, what will be its new angular momentum?

[00:05:58]So, as we know kinetic energy for a circular motion is equals to 1 by 2 I omega squared, correct?

[00:06:05]So, what can we say? Can we write Can we say that uh So, can we say that KE is equals to 1 by 2 L omega because we know that I is equals L is equals to I omega, right?

[00:06:19]So, using this equation we can write KE upon omega is proportional to L, right? Kinetic energy upon omega is proportional to L.

[00:06:29]Now, we as the question suggests kinetic energy is become 1 by 2. So, I'll just solve it here itself.

[00:06:35]So, KE has become 1 by 2. So, now the for this new value of uh angular momentum, we have 1 by 2 KE and uh 2 omega. So, now the final uh angular momentum becomes 1 by 4 times whatever was the initial value of angular momentum, right? So, it becomes L by 4.

[00:06:58]Now, moving forward two circular discs A and B have equal masses and equal thickness. But density D1 and D2 uh density is different, right? D1 is greater than D2. Now, if two objects have same mass and same thickness and if D1 if one object is denser than the other object, in that case what will happen?

[00:07:17]The uh what is the formula for density?

[00:07:19]How do we calculate density? Density is equals to mass per unit volume, right? So, uh if density of D1 is greater than density of D2, in that case and the mass is remaining mass is same.

[00:07:33]So, in that case uh volume one will be greater than volume two, right?

[00:07:41]Now, moving forward we have two circular discs A and B having equal masses and equal thickness, but density D1 and D2 uh are different of the two objects, and D1 is greater than D2. Now, if D1 is greater than D2, in that case, what will happen? Density and volume are uh same.

[00:07:58]We know that density is equals to mass per unit volume. So, if density is high, volume will be low. So, V1 will be less than V2, correct? And if volume is less, for any disc, what is volume? Volume is 2 pi r.

[00:08:14]Right? Volume will be dependent upon the radius into h, whatever is the height of the disc, correct? So, height is height is same for both.

[00:08:22]So, what can differ?

[00:08:24]2 pi r 1 h1 and r2 h2, right? So, if we already know height is same for both the cases, radius r1 will be less than r2, right?

[00:08:34]And what is the moment of inertia of a disc?

[00:08:37]Moment of inertia of a disc is 1 by 2 mr squared, right? Mass in both the cases are same. So, if r1 is less than r2, I1 IA will be less than IB, correct? Now, moving on, torque per unit of moment of inertia.

[00:08:52]So, torque per unit I, what is it called?

[00:08:55]We know that torque is equals to I alpha, right?

[00:08:59]So, torque per unit I I will be alpha, that is angular acceleration. Moving on, equation of displacement of a harmonic acceleration is 3 sin omega t plus 4 cos omega t. What will be the amplitude?

[00:09:11]Just take the uh magnitude of these two values and square it, 3 squared plus 4 squared, right? And you'll get your answer as 5, that is the amplitude.

[00:09:22]Now, in an SHM, when displacement is half the amplitude, the ratio of kinetic energy to potential energy is So, what is the formula for potential energy?

[00:09:31]Half kx squared.

[00:09:34]And what is the total energy of any SHM?

[00:09:37]That is 1/2 k a squared, correct? Now, it is given that at this point our kinetic energy is half the potential energy. Sorry, the amplitude is half the amplitude. So, the value of x is a/2. Correct? So, in that case, the potential energy and this is the total energy, right? The potential energy will be 1/2 k into a squared by 4, correct?

[00:10:05]Now, this will be the value of potential energy. And we know that kinetic energy is equals to potential or total energy minus potential energy. So, uh 1/2 k squared minus k a squared upon 8.

[00:10:22]So, that will give us what? Um 3/8 k a squared.

[00:10:31]That is equals to your kinetic energy, right? So, the ratio of kinetic energy is 3/8. And here we have 1/8 k a squared. So, that is 3:1, correct?

[00:10:42]Moving on.

[00:10:44]A spring of force constant k is cut into three equal parts. So, whenever we have a spring, and if we are cutting into three equal parts, now the shortest thing will be a string spring will be more stiff, right? It will have more restoration force. So, each string gets divided in each strings has its own uh spring constant becomes three times what was the initial value, okay? So, it becomes 3k. Now, moving on.

[00:11:07]The load of a 10 uh The load of 10 g increases the length of a light spring by 10 cm. And the spring con- We have to calculate the spring constant. Now, if you are saying that because of the this weight, the spring got elongated by 10 cm. So, this f is equals to kx.

[00:11:26]And x is equals to 10, right? Now, and because of this weight, the weight is 10 g. So, we know that weight F is equals to mg, right? So, mass is 100 and G is 9.8. That will be equal to kx. And x we already know is 10. Correct? Now, if we take all of this in standard units, we'll convert this 10 into mm and this 10 grams into kg. So, K will become This K becomes 10 in K into 0.01 is equals to 0.

[00:12:00]1 into 9.8.

[00:12:03]Right? Sorry, this will not be 0.1. This will be also be 0.1.

[00:12:11]0.

[00:12:12]1. So, this and this gets cancelled and you get the value of K as 9.8. That is option A.

[00:12:18]Okay? Moving on.

[00:12:21]If the length of a simple pendulum is increased fourfold, what is the time period? Now, what is the time period of a simple pendulum?

[00:12:27]2 pi under root L upon G. Now, if length increases by four times, so the current The new time period will be what? 2 pi into 4L upon G. So, that is Once this four comes out of the root, that that that time you'll get two into initial time period, right? This four will come out and get multiplied by two.

[00:12:48]So, we get two into initial time period.

[00:12:50]That is 2T. Now, a hollow copper sphere is given a positive charge. The electric field inside the sphere is So, we have already discussed inside a hollow sphere, there is no electric field here, right?

[00:13:02]Outside you'll feel it. In a solid sphere, there will be electric field inside the sphere, but in a hollow shell structure, there is no electric field inside it, okay? So, that will be zero.

[00:13:12]Now, a charge Q is enclosed by a Gaussian spherical surface. So, there's a spherical surface and there's a charge Q inside it.

[00:13:19]Okay?

[00:13:21]of R. If the radius is doubled, the outward electric flux through the surface Now, even if we increase the radius to double, the charge enclosed by this uh Gaussian surface is still Q. So, that remains the same.

[00:13:35]When the capacitor C1, C2, and C3 are connected in parallel, the formula for equivalent capacitance will be just normally we uh in for the capacitors, we just normally add it in parallel, so it will be C1 + C2 + C3, right?

[00:13:49]The potential of two plates of a capacitor are +10 V and -10 V. What is the potential difference between them?

[00:13:55]So, first plate has 10 V minus the potential of the second plate, that is -10 V.

[00:13:59]The total potential difference will be 20 V, right? So, option C.

[00:14:04]Now, an electric field can affect uh what can it affect? So, first, X-rays, they have no charge, so it cannot affect that.

[00:14:12]Neutrons, they are neutral already.

[00:14:15]No charge. Gamma rays also have no charge. So, what are we left with?

[00:14:19]Cathode ray. Cathode ray is a string of electrons.

[00:14:25]Okay? So, these are negatively charged.

[00:14:28]So, only charged particles can get affected by electric field, right? So, the our option is cathode ray. Now, a convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. So, what will be the power power of the combination?

[00:14:43]So, for the convex lens what convex lens have positive focus, so power here the power one of a convex lens will be 1 by 40. We convert this centimeter to meter, right? So, that will become 0.4.

[00:14:56]And the power of the second lens since it is a concave lens, the power will since the focal length is negative, the power will also be negative. That is 1 upon 0. 25, right?

[00:15:06]Now, this and this 25 so, you get four.

[00:15:11]And here four, so 2.5. Now, what will be the final power?

[00:15:17]1.5, so option B, right?

[00:15:20]Now, the critical angle is maximum when the light travels from So, this happens whenever the the the ratio between the density or the of the two forms is almost equal to one. In that case, the critical angle is maximum. So, that will be in the case of glass to water. Okay?

[00:15:39]When light travels from one medium to another, the characteristic that does not change is See, when light travels, speed also gets affected because of the medium. So, if there is a denser medium, speed will be less. If it is a If there is a rarer medium, speed will be more. Wavelength is also dependent upon the medium. And amplitude of how fast or how high or low the wave size will be. That also depends upon the uh medium. But what does not depend upon the medium is the frequency. So, frequency remains unchanged. Next.

[00:16:06]An object lies 1 m in front of the mirror. The mirror moves 10 cm towards the object. So, we have an object. We have a mirror. And in front in 1 m away from it, we have our object. So, image will be formed here. So, this will also be 1 m. This will also be 1 m. Now, the mirror moves 10 cm towards the object.

[00:16:24]So, the mirror was moved here.

[00:16:27]Right?

[00:16:29]This, let's say, is 1 cm. Now, uh the new distance between the object and the image will be So, now this distance left is 0.9 m. Correct? So, image also here will be formed at distance 0.9 m. So, distance between object and image will be 0.9 into two. That is 1.8.

[00:16:48]Optical fibers What principle does it work on? So, optical fibers are wires like this. They work on the fact or principle of total internal reflection.

[00:16:55]So, waves are sent and they are They are made in such a order that the Whatever reflection of waves happen, it The whole reflection gets reflected inside the system only. Okay? The critical angle is The angle of reflection is more than the critical angle. So, optical fibers works on the principle of TIR. Okay?

[00:17:13]Now, moving on.

[00:17:15]The source and the sink temperature of a Carnot engine are 40 K and 300 400 K and 300 K, okay? It is asking for the efficiency. So, what is the formula for efficiency? The for mu is equals to 1 minus the temperature of the sink.

[00:17:31]That is temperature of the so sink that is 300 divided by temperature of the source that is 400. So, that will give you uh 1 by 4, that is 25% right? So, option B.

[00:17:43]Moving forward, a gram of water at 100° C is converted into steam at 100° C. So, So, what amount of heat is required?

[00:17:52]This is asking about latent heat of fusion.

[00:18:01]Sorry, of vaporization.

[00:18:05]Okay? Now, this can only be only be solved if you're already aware of the answer. That is you have already come across this question. So, because you have to remember the value of latent heat of water. Okay? That is 540 K.

[00:18:17]Now, a sound wave has a frequency of 2 Hz and a wavelength of 35 cm. An observer is 1.4 km away. After what time will the After what time will the observer hear the sound?

[00:18:31]So, the speed of the sound will be what?

[00:18:34]Frequency into lambda, right? Frequency into lambda or the wavelength. So, frequency is given to us as 2 kHz. 2 into 10 to the power 3 and the wavelength is 35 divided by 100, right? It is It is given in centimeters, so we'll convert it into meters.

[00:18:51]So, that gives us a value of what? 35 into 2 into the power 700 m per second.

[00:18:57]Now, the observer is at 1 1.4 km away.

[00:19:00]So, what will be the time taken?

[00:19:03]2 seconds, right? So, the answer is B.

[00:19:07]The ratio of excess pressure inside two soap bubbles with radii of ratio 2 is to 1 is What is the value of expression inside a bubble? That is 2t upon r, right? So, the ratio of the pressure the ratio of the radii is 2:1, what will be the ratio of pressure?

[00:19:23]Since the pressure is inversely proportional to radius, so the ratio of the pressure will be 1:2. Correct? So, answer is A.

[00:19:34]Moving on.

[00:19:35]A body of mass 50 kg has a velocity reduced from 20 m to 5 m by a restoring force in 5 seconds.

[00:19:42]So, initial velocity was 20, final velocity is 5, and time time period is also 5 seconds. So, it is asking about the magnitude of the restoring force. So, acceleration will be what?

[00:19:54]Uh 5 - 20 / 5, that is 3 m/s ^ 2 -3 m/s ^ 2 to be specific.

[00:20:05]Now, and the mass is also given to us that is 50 kg. So, what is the force?

[00:20:09]Force is equal to mass into acceleration.

[00:20:12]That is 50 into 3. So, uh 50 into 3 that will give you 150. Now, here we are not taking the negative sign because it is already mentioning it is a resisting force. So, we already know it is a negative sign. So, instead we are taking it as just 3, okay? And the force is 150 N.

[00:20:29]Now, apparent frequency heard by a listener moving away from a stationary source is 10% less than the actual frequency. Now, if the speed of the sound is 330 m, what is the velocity of the listener? So, the frequency of a moving in case when the observer is moving is equal to what?

[00:20:47]Is equal to f upon uh velocity of the sound minus velocity of the observer divided by velocity of the sound, right? Now, we we can say that it is already mentioning that the frequency heard by the listener is 10% less. So, the final frequency is 0.9 times the initial frequency.

[00:21:08]So, can we write f' upon f is equals to 0.9? Now, if we take this f down side, uh 0.9 is equals to uh v 1 minus v0 upon v, correct?

[00:21:21]So, now, uh v0 is the velocity of absorber, v is the speed of sound that is already given to us, 330, right? So, 0.9 is equals to 1 minus v0 upon 330, correct?

[00:21:35]Now, let's solve it out. So, uh 330 into 0.9 is equals to 330 minus v0, correct? Now, if you multiply these two values, you will get 297 is equals to 330 minus v0. So, you'll get the value of v0 is equals to 33 m per second. That is your option A.

[00:22:01]Moving forward, a constant wire is used in making a standard resistance.

[00:22:05]Because, see, uh resistance uh is mostly dependent upon the uh the only uh non-moving factor of a resistance is the resistivity, that is rho l upon a. This is a constant what uh different types of element. And the only thing that influences this resistance is your temperature.

[00:22:23]For a constant wire, uh the temperature coefficient of resistance, it is negligible. So, it will not be affected by changing temperatures. That is why it is used to make standard resistance, okay? Now, drift velocity of electron in the conductor, so this also you cannot be uh knowing uh like you cannot be solving it in the exam. Drift uh you will have to gone through some similar kind of questions to actually know that the drift velocity of electrons in a conductor is of the order 10 to the power 4 or even 10 to the power minus 3 also. So, if in that same range, okay?

[00:22:53]Unit of specific resistance is What is specific resistance? This value of ohm, okay? So, if you know r is equals to rho l upon a, So, that is ohm is equals to the value whatever will be of rho.

[00:23:06]L is length is in meter and area is in meter square.

[00:23:10]Correct? So, rho will be ohm meter.

[00:23:13]So, option B.

[00:23:15]Okay? Now, moving on.

[00:23:17]Wheatstone bridge is given to us P1 Q P Q R and S, okay? And it is saying that the bridge is not balanced. So, how do we balance it?

[00:23:24]So, P upon Q should be equal to R upon S, right?

[00:23:30]So, what is the ratio P upon Q is 10 upon 5?

[00:23:34]Is that is not equal to 4 upon 4, right?

[00:23:37]So, how can we balance it out? If we add another 5 ohm resistance to this Q, these two also will cancel out to give one, right? So, we can add 5 ohm in series with Q. So, option D. Okay? Now.

[00:23:52]A potentiometer measures potential more accurately because uh here, measures potential in closed circuit? No. Uses high galvanometer sensitivity? No. Measures potential in open circuit at null point. See, whenever we measure potential because of a with using a potentiometer, we try to make a Wheatstone bridge out of it, right? So, what the whenever there is the whenever it actually pinpoints the actual potential of a device, at that point there is no current flowing through it, right? It calculates at null point. So, because of that it does not consumes any part of the potential. So, it gives a more exact reading out of it.

[00:24:28]Now, moving on.

[00:24:30]The word magnetism is derived from iron ore called magnetite, okay?

[00:24:36]A jet craft flies due south at 300 m/s.

[00:24:40]So, velocity is 300.

[00:24:41]Where the vertical component of Earth's magnetic field is 80 microtesla, okay?

[00:24:46]So, the value of B is 80 into 10 to the power -6.

[00:24:51]And the wind span length is 25 m. So, how much EMF will be induced? The value of induced EMF is what? B into L cross V.

[00:25:00]So, the 80 into 300 into 25. If you multiply all of that, 80 into 25 into 300 into 10 to the power -6, you'll get the value as 0.6 volts.

[00:25:13]So, option B. Okay?

[00:25:15]Now, two pure inductors each of self-inductance L are connected in parallel far apart. What will be the total inductance? So, when inductors are connected in parallel, to calculate total inductance, what do we do? 1 by L1 + 1 by L2, right? So, I mean, 1 by L + 1 by L. That is 2 by L is equals to 1 by L equivalent. So, L equivalent becomes L by 2. So, correct option is C.

[00:25:42]An inflated balloon with a heavy rock sinks in water. As it sinks, the buoyant force So, see, this is a uh tank in which we have a balloon, and this balloon is going down. As it will start going down, what will happen? The pressure will keep on increasing on the balloon.

[00:25:56]Now, we know that PV is equals to constant, right?

[00:26:00]By Boyle's law, we know that. So, if pressure is increasing, volume will start to decrease, right? So, if volume of the balloon will start to decrease because there's gas inside the balloon, right? So, that if start if it starts decreasing, so the amount of water this balloon will be displacing displacing will also start decreasing, right? So, the buoyant force is dependent upon what? The amount of water the object is displacing. So, if the volume of the displaced volume is reducing, the buoyant force also will reduce, right?

[00:26:28]So, that is why the buoyant force decreases. Now, in a Carnot cycle, when heat is absorbed from a hot source by working gas, what happens? The this process will include isothermal expansion. So, what it happens is, let's say that we have a piston for a random example, okay? Now, this piston is compressing gas, okay?

[00:26:50]Uh so, I'm not compressing, expanding So, for any kind of for expansion to happen, if the expansion happens by the work done of this gas. So, this there's gas inside. This gas is trying to push the piston. So, the piston moved here, okay?

[00:27:05]So, because of that, what will happen?

[00:27:07]The temperature will drop down because the gas expanded, right? But, it's from the source of the heat from the heat source, we are constantly supplying uh heat to maintain the temperature of this gas. So, the temperature is remaining constant, but expansion is also happening. So, this is isothermal expansion, okay?

[00:27:22]Now, the value of regarding potential uh needed to stop a photoelectric injection from a neutral from a metal uh with work function 1.2 electron volts and light of energy 2 electron volts will be So, we know that the formula is KE is equals to HV minus phi, okay? The value of HV or the uh energy, or you can also write it as KE is equals to E minus phi.

[00:27:46]So, it is already given to us the energy is 2 electron volts and the work function phi is 1.2, right? So, if we subtract 2 minus 1.2, you will get what?

[00:27:55]0.8 volts. That is your option C, correct? Now, moving forward, according to Bohr's atomic model, the electrons revolves in orbits where So, in according to Bohr's model, uh it was given that MVR or the electrons will only revolve in orbits which are which have the energy equals to NH upon 2 pi, right? So, it can only revolve in orbits which are multiple of NH upon 2 pi. So, that is your option B, okay?

[00:28:23]Binary representation of decimal 45.

[00:28:25]Now, how can we write 45? 45 is equals to 32 plus 8 plus 4 plus 1. That is 2 to the power 5 plus 2 to the power 3 plus 2 to the power 2 plus 2 to the power 0, right? So, we have 0 1 2 3 4 5.

[00:28:45]This will become one zero, one, one, zero, one. So, 101101.

[00:28:53]101101, that is your option B.

[00:28:57]Decimal representation of 10 11 will be So, 2 to the power zero plus 2 to the power one plus 2 to the power three, right?

[00:29:07]Because 2 to the power 2 is already zero. So, 1 plus 2 plus 8.

[00:29:13]So, we'll get the answer as 11. So, option C is correct here. Now, four colored metallic articles at the same temperature are allowed to cool.

[00:29:22]Which will cool fastest? So, we have blue, red, black, white. Now, see, black body is the fastest to cool, right?

[00:29:27]Because it emits all the heat. So, it will cool the fastest.

[00:29:31]Now, resistance of a wire of diameter 6 mm is 5 ohm. If it is drawn until diameter becomes 3 mm, what will be its new resistance? Now, if the diameter has been reduced from 6 mm to 3 mm, that is half, what will happen?

[00:29:46]So, we know that resistance is inversely proportional to 1 upon area square, right?

[00:29:51]And now, if diameter has become half, the radius will also would have become half. So, the resistance is proportional to 1 by 4 times the diameter cos square or radius cos square, correct?

[00:30:02]Now, not square, actually it should be power four, right? Because area is 2 pi r square.

[00:30:09]Like pi r square, right? Now, so the resistance is proportional to the power of four of diameter or radius, right?

[00:30:18]Now, if diameter has become half, so that means r' is equals to 1 by d upon 2 to the power four. So, 2 to the 16, so r' is equals to 16 times whatever the value of r was, right? So, r was already five. 5 into 16, you'll get your answer as 80, okay?

[00:30:41]No.

[00:30:42]An elastic spring has a spring constant K. When it is cut into three equal parts, and all three parts are connected in parallel, what will be the effective force constant? Now, as we discussed before, if the spring is cut into three equal parts, each part will have a spring constant of 3K. Now, if you're attaching these three springs in parallel combination, what will happen?

[00:31:02]We'll just add all the three spring constants, 3K + 3K + 3K, and you get finally as 9K. So, 9K is the spring constant of the new spring setup.

[00:31:12]A body executing SHM with an amplitude of 0.1 mm meter, at what displacement from the mean position is the potential energy equal to kinetic energy? Now, uh potential energy is equal to kinetic energy at X is equal to amplitude upon under root two.

[00:31:28]This, either you will be knowing, or you can also derive it, okay? So, what you can do is See, uh one second.

[00:31:40]Okay, this is not working. Anyway, so I'll show you with an example here.

[00:31:45]Now, so kinetic energy of a spring is one uh potential energy total energy minus potential energy, correct? And we know that the potential energy is equal to 1/2 KX squared.

[00:32:00]And uh total energy is equal to 1/2 KA squared, correct?

[00:32:07]Now, so kinetic energy will be what? 1/2 KA squared minus 1/2 KX squared.

[00:32:15]This should be equal to So, that that will be equal to your kinetic energy, right? And this kinetic energy should be put equal to the potential energy at that point of time. So, 1/2 KX squared. So, if we just take it to the other side, 1/2 KA squared is equal to KX squared. K and K will get canceled.

[00:32:34]And A squared upon two is equals to x squared. So, that implies x is equals to a upon under root two. So, at x at the displacement amplitude upon under root two at that point the kinetic energy and potential energy will be equal. So, now in the question we have been given amplitude is 0.1 divided by under root two.

[00:32:56]So, that you will get or just multiply the whole thing by under root two into under root two and you will get uh 0.1 by two into under root two. That is 0.05 under root two. So, option C. Okay, sorry.

[00:33:13]Option C.

[00:33:15]Moving on. A boat crosses a river with velocity of 8 km relative to water. If the resultant velocity is 10, what is the velocity of river?

[00:33:23]So, if the resultant velocity is 10, that would be equal to uh the velocity of uh boat plus the velocity of river.

[00:33:31]So, if you just take the amplitude squared of This is the resultant velocity is 10, velocity of river is given as eight. The square of eight. And velocity of current uh So, and we have to find out the velocity of the river that is let's say x squared. Okay?

[00:33:47]So, uh we'll just take 100 is equals to eight squared plus x squared.

[00:33:53]So, uh 36 is equals to x squared. So, that implies velocity of the river x is 6 km/h. That is your option B.

[00:34:03]Lastly, if a Carnot engine operates at the source temperature of 127° C and a sink temperature of 27° C, what will be its efficiency? Now, uh to calculate that convert these two into your uh Kelvin scale.

[00:34:17]So, 127 + 273 that is zero zero 400. And 27 + 273 that will give you another zero zero and 300. Isn't it the same question as we first solved? So, that will be 1 - 300 by 400. That is giving you 1 upon 4, that is 25%. Right? So, that was about it with this guess paper. I hope you are well prepared for your upcoming exams.

[00:34:49]And try solving as much as questions at this point of time. Try going through PYQs and all the necessary And more The more you practice of time that will be better for you. So, stick to solving more and more questions at this point. Try different types of question, guys, okay? All the best for your exams. Thank you, students.