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2 kg and 3 kg blocks are placed on a smooth horizontal surface and connected by a spring which is unstretched initially. The blocks are imparted velocities as shown in the figure. 3. Maximum speed of 2kg block in the subsequent motion will be a. 𝑣_0 b. 2𝑣_0 c. 3𝑣_0 d. 4𝑣_0

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2 kg and 3 kg blocks are placed on a smooth horizontal surface and connected by a spring which is unstretched initially. The blocks are imparted velocities as shown in the figure. 2. Maximum speed of 3kg block in the subsequent motion will be a. 𝑣_0 b. 2𝑣_0 c. 3𝑣_0 d. 4𝑣_0

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2 kg and 3 kg blocks are placed on a smooth horizontal surface and connected by a spring which is unstretched initially. The blocks are imparted velocities as shown in the figure. The maximum energy in the spring in the subsequent motion will be . a. 5𝑣_0^2 b. 15𝑣_0^2 c. zero d. 10𝑣_0^2

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A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact lasts for time Δt. 1. The average elastic force acting on the ball is "m(u+v)" /"Δt." 2. The average elastic force acting on the ball is" 2m(u+v)" /"Δt." 3. The kinetic energy of the ball increases by 2mu(u+v). 4. The kinetic energy of the ball remains the same after the collision.

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A particle moving with kinetic energy 3 J makes an elastic head-on collision with a stationary particle which has twice its mass. During the impact,  (a) the minimum kinetic energy of the system is 1 J  (b) the maximum elastic potential energy of the system is 2 J  (c) momentum and total energy are conserved at every instant  (d) the ratio of kinetic energy to potential energy of the system first decreases and then increases

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A blast breaks a body initially at rest of mass 0.5kg into three pieces , two smaller pieces of equal mass and the third double the mass of either of small piece . After the blast two smaller masses move at right angles to one another with equal speed . Find the statements that is/are true for this case assuming that the energy of blast is totally transferred to masses. All the three pieces share the energy of blast equally The speed of bigger mass is √2 times the speed of either of the smaller mass The direction of motion of bigger makes an angle of 135° with the direction of smaller pieces The bigger pieces carries double the energy of either pieces

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Two charges moving under their only own mutual attraction separated by large distance initially. Then choose the correct statement(s) 1. If both are free, mechanical energy is conserved. 2. If one is fixed and other is free, mechanical energy is conserved. 3. If one is fixed and other is free, momentum is conserved. 4. If both are free momentum is conserved.

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X and Y component of acceleration of centre of mass are : 𝑎_(𝑐𝑜𝑚 𝑥)=(𝑚_1 𝑚_2 𝑔)/(𝑚_(1+) 𝑚_2 ) 𝑎_(𝑐𝑜𝑚 𝑥)=(𝑚_1 𝑚_2 𝑔)/〖𝑚_(1+) 𝑚_2〗^2 𝑎_(𝑐𝑜𝑚 𝑦)= 〖(𝑚_2/(𝑚_(1+) 𝑚_2 ))〗^2g 𝑎_(𝑐𝑜𝑚 𝑦)=(𝑚_2 𝑔)/〖𝑚_(1+) 𝑚_2〗^2

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In head on elastic collision of two bodies of equal masses, The velocities are interchanged The speeds are interchanged The momenta are interchanged The faster body speeds up and the slower body slows down

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For a two body system in absence of external forces, the kinetic energy as measured from ground frame is 𝐾_0 and from centre of mass frame is 𝐾_𝐶𝑀. Pick up the CORRECT statement. 1. The kinetic energy as measured from center of mass frame is least 2. Only the portion of energy 𝐾_𝐶𝑀 can be transferred from one form to another due to internal changes in the system. 3. The system always retains at least 𝐾_0- 𝐾_𝐶𝑀 amount of kinetic energy as measured from ground frame irrespective of any kind of internal changes in the system. 4. The system always retains at least K c m 𝐾 𝑐 𝑚 amount of kinetic energy as measured from ground frame irrespective of any kind of internal changes in the system.

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A man of mass `80 kg` stands on a plank of mass `40 kg`. The plank is lying on a smooth horizontal floor. Initianlly both are at rest. The man starts walking on the plank towards north and stops after moving a distance of `6 m` on the plank. Then 1. The centre of mass of plank-man system remains stationary 2. The plank will slide to the north by a dsitance `4m` 3. The plank will slide to the south by a distance `4 m` 4. The plank will slide to the south by a distance `12 m`

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Assuming potential energy ‘U’ at ground level to be zero. All objects are made up of same material. UP = Potential energy of solid sphere UQ = Potential energy of solid cube UR = Potential energy of solid cone US = Potential energy of solid cylinder US > UP  (B) UQ > US  (C) UP > UQ (D) US > UR

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The centre of mass of a system of particles is at the origin. Which of the following statement is incorrect . The number of particle to the righ of the origin is equal to the number of particles to the left The total mass of the particles to the right of the origin is same as the total mass to the left of the origin The number of particles on X-axis should be equal to the number of particles on Y-axis If there is a particle on the positive X-axis, there must be at least one particle on the negative X-axis.

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A rocket of mass 4000 kg is set for vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude 19.6 m/s2 . [Exhaust speed of fuel = 980 m/s.]. (1) 240 kg s –1  (2) 60 kg s –1  (3) 120 kg s –1  (4) 130 kg s –1 

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A balloon having mass 'm' is filled with gas and is held in hands of a boy. Then suddenly it gets released and gas starts coming out of it with a constant rate. The velocity of the ejected gas is 2m/s with respect to the balloon. Find out the velocity of the balloon when the mass of gas is reduced to half :( neglect gravity) ln2 2ln4 2ln2 None of these

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A wagon filled with sand has a hole so that sand leaks through the bottom at a constant rate λ. An external force 𝐹 ⃗ acts on the wagon in the direction of motion. Assuming instantaneous velocity of the wagon to be 𝑉 ⃗ and initial mass of system to be m0, the force equation governing the motion of the wagon is 𝐹 ⃗ = 𝑚_0 (𝑑𝑉 ⃗" " )/𝑑𝑥 + λ𝑉 ⃗ 𝐹 ⃗ = 𝑚_0 (𝑑𝑉 ⃗" " )/𝑑𝑥 - λ 𝑉 ⃗ 𝐹 ⃗ = (𝑚_0−"λ " 𝑡)(𝑑𝑉 ⃗" " )/𝑑𝑥 (𝑚_0−"λ " 𝑡)(𝑑𝑉 ⃗" " )/𝑑𝑥 + λ 𝑉 ⃗

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The carriage of mass M has constant initial velocity u along a straight horizontal track when at t=0. it starts raining. The rain drops have a vertical velocity u′ and result into addition of mass in per second to the carriage. The velocity of ear after T second of start of rain is (Asume frictionlews surface): see the sheet

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An open water tight railway wagon of mass 5 × 〖"10" 〗^"3" kg coasts at an initial velocity 1.2 m/s without friction on a railway track. Raindrops fall vertically down wards into the wagon. The velocity of the wagon after it has collected 〖"10" 〗^"3" kg of water will be 0.5 m/s  (B) 2 m/s  (C) 1 m/s  (D) 1.5 m/s

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A bead of mass m and diameter d is sliding back and forth with velocity v on a wire held between two right walls of length L. Assume that th ecollisions with the wall are perfectly elastic and there is no friction. The average force that the bouncing bead exerts on the one of the walls is : mv^2/(𝑙−𝑑) mv^2/(𝑙+𝑑) 〖2mv〗^2/(𝑙−𝑑) 〖2mv〗^2/(𝑙+𝑑)

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A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest . The kinetic energy of the balls after the collision is three fourths of the original . Find the coefficient of restitution 1. 𝑣/(√3) 2. √3 3. (√3)/(√2) 4. (√2)/(√3)

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A mass m moves with a velocity v and collides in-elastically with another identical mass at rest . After collision the first mass moves with velocity 𝑣/(√3) in a direction perpendicular to the initial direction of motion . Find the speed of second mass after collision 2𝑣/(√3) 𝑣/(√3) (𝑣√2)/(√3) The situation of the problem is not possible without external impulse

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Two bodies A and B , collide as shown in figures a and b below .circle the true statement : (a) (b) They exert equal and opposite forces on each other in (a) but not in (b) They exert equal and opposite forces on each other in (b) but not in (a) They exert equal and opposite forces on each other in (a) and (b) The forces are equal and opposite to each others in a but only the component of the forces parallel to the velocities are equal in b .

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A particle is projected from a smooth horizontal surface with velocity v at an angle 𝜃 from horizontal . Coefficient of restitution between the surface and ball is e . The distance of the point where ball strikes the surface second time from the point of projection is . (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 e^2))/𝑔 (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 e^4))/𝑔 (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 e^3))/𝑔 (〖v^2 𝑣𝑠𝑖𝑛2𝜃〗⁡〖(1+〗 𝑒))/𝑔

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A ball is projected from ground with a velocity v at an angle 𝜃 to the vertical . On its path it makes an elastic collision with a vertical wall and returns to ground . The total time of flight of the ball is 2𝑣𝑠𝑖𝑛𝜃" " /𝑔 2𝑣𝑐𝑜𝑠𝜃" " /𝑔 2𝑣𝑠𝑖𝑛2𝜃" " /𝑔 2𝑣𝑐𝑜𝑠𝜃" " /𝑔

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A ball is sticks a smooth horizontal ground at an angle 45° with the vertical . What can not be the possible angle of its velocity with the vertical after the collision .e≤1 45° 30° 53° 60°

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A ball collide with an inclined plane of inclination 𝜃 after falling through a distance h .if it moves horizontally just after the impact , the coefficient of restitution is . tan^2⁡𝜃 cot^2⁡𝜃 tan⁡𝜃 cot 𝜃

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A ball of mass m approaches a moving wall of infinite mass with a speed v along the normal to the wall. The speed of the wall is u towards the ball . The speed of the ball are after elastic collision with wall is U + v away from the wall 2u + v away from the wall |𝑢−𝑣 | away from the wall |𝑣−2𝑢 | away from the wall

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A boy hits a baseball with a bat and imparts an impulse J to the ball . The boy hits the ball again with the same force , except that ball and bat are in contact for twice the amount of time as in the first hit . The new impulse equals : Half the original impulse The original impulse Twice the original impulse Four times the original impulse

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A block of wood of mass 9.8kg is suspended by a string . A bullet of mass 200gm sticks horizontally with a velocity of 200m/s and gets embedded in it . The maximum height attained by the blocks is 0.1m 0.2m 0.3m 0

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A block of wood of mass 9.8kg is suspended by a string . A bullet of mass 200gm sticks horizontally with a velocity of 200m/s and gets embedded in it . The maximum height attained by the blocks is 1. 0.1m 2. 0.2m 3. 0.3m 0

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moment of inertia all questions

https://youtu.be/Bf2OuJuxPqQ 1. Three balls of masses 2kg ,4kg and 6kg respectively are arranged at centre of the edges of an equilateral tringle of side 2m . The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of tringle will be ……………………kg𝒎^𝟐 (2024 ) 2.Ratio of radius of gyration of hollow sphere to that of a solid cylinder of equal mass , for moment of inertia about their diameter axis AB as shows in figure is √(𝟖/(𝒙 )) . The value of x is : (2024) 3.Two identical spheres each of mass 2kg and radius 50cm are fixed at the ends of a light rod so that the separation between the centre is 150cm , then moment of inertia of the system about an axis perpendicular to rod and passing through its middle point is 𝒙/𝟐𝟎 kg𝒎^𝟐 where the value of x is ……………2024 4.Four particles each of mass 1 kg are placed at four corners of a square of side 2m . Moment of inertia of system about an axis perpendicular to its plane and passing through one o...
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A ball of mass m approaches a moving wall of infinite mass with a speed v along the normal to the wall. The speed of the wall is u towards the ball . The speed of the ball are after elastic collision with wall is U + v away from the wall 2u + v away from the wall |𝑢−𝑣 | away from the wall |𝑣−2𝑢 | away from the wall

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A boy hits a baseball with a bat and imparts an impulse J to the ball . The boy hits the ball again with the same force , except that ball and bat are in contact for twice the amount of time as in the first hit . The new impulse equals : Half the original impulse The original impulse Twice the original impulse Four times the original impulse

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Moment of inertia of a uniform circular disc about a diameter is `I`. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be. 1999 A. `6 I` B. 4 I C. 2 I D. 8 I

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Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shell about XX' axis is 2015 16/5MR2 4 MR2 11/5MR2 3MR2

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From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre? 2016 (a) 11 MR2/32 (b) 9 MR2/32 (c) 15 MR2/32 (d) 12MR2/32

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Four identical thin rods each of mass M and length l form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is 2009 (a) 2/3 Ml2 (b) 13/3 Ml2 (c) 1/3 Ml2 (d) 4/3 Ml2

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The moment of inertia of a disc of mass M and radius R about an axis which is tangential to the circumference of the disc and parallel to its diameter, is 1. 5/4MR2 2. (2/3)MR2 3. (4/5)MR2 4. (2/3)MR2

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The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is : 2/5 〖𝑀𝑅〗^2 3/5 〖𝑀𝑅〗^2 1/2 〖𝑀𝑅〗^2 〖𝑀𝑅〗^2

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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is : 2011 (a) I0 + ML2/2 (b) I0 + ML2/4 (c) I0 + 2ML2 (d) I0 + ML2

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The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through. 2012 B C D A

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In a rectangle ABCD (BC=2AB). The moment of inertia is minimum anout which the axis will be 1993 BC BD HF EG

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ABC is a traiangular plate of uniform thickness. The sides are in the ratio shown in the figure. "I" _"AB" , "I" _"BC"   and "I" _"CA"   are the moments of inertia of the plate about AB, BC and CA respectively. Which one of the following relations is correct? 1995 "I" _"AB" > "I" _"BC" "I" _"BC" > "I" _"AB" "I" _"AB" + "I" _"BC"   = "I" _"CA" "I" _"CA" IS MAXIMUM

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There is a flat uniform triangular plate ABC, sides AB= 4 cm, BC= 3 cm and ∠ABC=90∘. The moment of inertia of the plate about AB, BC and CA as axis are I1, I2 and I3 respectively. Which one of the following is true? 𝐼_3> 𝐼_2 𝐼_2> 𝐼_1 𝐼_3> 𝐼_1 𝐼_1> 𝐼_2

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A composite disc to be made using equal masses of aluminimum and iron so that it has as high a moment of inertia as possible. This possible when. 2002 The surfaces of the discs are made of iron with aluminium inside The whole of aluminum is kept in the core and the iron at the outer rim of the disc The whole of the iron is kept in the core and the aluminium at the outer rim of the disc The whole disc is made with thin alternate sheets to iron and aluminimum.

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Three particles. each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be :2004 2/3 〖𝑀𝐿〗^2 3/4 〖𝑀𝐿〗^2 2〖𝑀𝐿〗^2 5/4 〖𝑀𝐿〗^2

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The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and a circular ring of the same radius about a tangential axis in the plane of the ring is : 2004 1 : √(𝟐 ) 1 : 3 2 : 1 √(𝟓 ):√(𝟔 )

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A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is : 2008 (1) ML2/6 (2) √2ML2/24 (3) ML2/24 (4) ML2/12

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Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ω0 is minimum, is given by :2015 𝑚_1/𝑚_2 L 𝑚_2/𝑚_1 L 𝑚_2/(𝑚_1+𝑚_2 ) L 𝑚_1/(𝑚_1+𝑚_2 ) L

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The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are : 2013 (1) 1 : √2 (2) 3 : 2 (3) 2 : 1 (4) √2 : 1

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From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' times 'MR2'. Then the value of 'K' is : 2021 ncert page 163 𝟏/𝟖 𝟑/𝟒 𝟕/𝟖 𝟏/𝟒

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The ratio of the radius of gyration of thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is : 2022 ncert 165 √(𝟐 ): 1 4 : 1 1 : √𝟐 2 : 1

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The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g〖𝒄𝒎〗^𝟐 . The length of the 400g rod is nearly : 2024 page 165 8.5cm 17.5 cm 20.7cm 72cm

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The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g〖𝒄𝒎〗^𝟐 . The length of the 400g rod is nearly : 2024 page 165

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