Question 1 :
A rod of mass {tex} m {/tex} and length {tex} l {/tex} is bent in to shape of {tex} L . {/tex} Its moment of inertia about the axis shown in figure<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0e74ed6e36502132f394"><br>

Question 2 :
The centre of mass of three bodies each of mass {tex} 1 \mathrm { kg } {/tex} located at the points {tex} ( 0,0 ) , ( 3,0 ) {/tex} and {tex} ( 0,4 ) {/tex} in the XY plane is

Question 3 :
A solid homogeneous sphere is moving on a rough horizontal surface partly rolling and partly sliding. During this kind of motion of the sphere

Question 4 :
There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is {tex} \mathrm { C } _ { 1 } , {/tex} while the centre of mass of the 'compartment plus passengers' system is {tex} \mathrm { C } _ { 2 } {/tex}. If the passengers move about inside the compartment then

Question 5 :
A particle moving in a circular path has an angular momentum of {tex}\mathrm L{/tex}. If the frequency of rotation is halved, then its angular momentum becomes

Question 6 :
Point masses {tex} 1,2,3 {/tex} and {tex}4{/tex} kg are lying at the points {tex} ( 0,0,0 ) , ( 2,0,0 ) , ( 0,3,0 ) {/tex} and {tex} ( - 2 , - 2,0 ) {/tex} respectively. The moment of inertia of this system about {tex} X {/tex} -axis will be

Question 7 :
The moment of inertia of a uniform circular disc (figure) is maximum about an axis perpendicular to the disc and passing through<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0d67ed6e36502132f343"><br>

Question 8 :
One solid sphere {tex} A {/tex} and another hollow sphere {tex} B {/tex} are of same mass and same outer radii, Their moments of inertia about their diameters are respectively {tex} I _ { A } {/tex} and {tex} I _ { B } {/tex}, such that

Question 9 :
From a disc of radius {tex} \mathrm { R } {/tex} and mass {tex} \mathrm { M } {/tex}, a circular hole of diameter {tex} \mathrm { R } {/tex}, whose rim passes through the centre is cut. What is the radius of gyration of the remaining part of the disc about a perpendicular axis, passing through the centre?

Question 10 :
The moment of inertia of wheel about the axis of rotation is 3.0 MKS units. Its kinetic energy will be 600 J if period of rotation is

Question 11 :
A toy car rolls down the inclined plane as shown in the fig. It loops at the bottom. What is the relation between Hand h?<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0fc44faa335027dc7819"><br>

Question 12 :
A body rolls down an inclined plane. If its kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is

Question 13 :
A billiard ball of mass {tex} m {/tex} and radius {tex} r , {/tex} when hit in a horizontal direction by a cue at a height {tex} h {/tex} above its centre, acquired a<br>linear velocity {tex} v _ { 0 } . {/tex} The angular velocity {tex} \omega _ { 0 } {/tex} acquired by the ball is<br>

Question 14 :
Two masses {tex} m _ { 1 } {/tex} and {tex} m _ { 2 } {/tex} are connected by a massless spring of spring constant {tex} k {/tex} and unstretched length {tex} \ell . {/tex} The masses are placed on a frictionless straight channel, which are consider our {tex} x {/tex} -axis. They are initially at {tex} x = 0 {/tex} and {tex} x = \ell {/tex}<br>respectively. At {tex} t = 0 , {/tex} a velocity {tex} v _ { 0 } {/tex} is suddenly imparted to the first particle. At a later time {tex} t , {/tex} the centre of mass of the two masses is at:<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5d5e83e906864d5bec7be6b1">

Question 15 :
A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,

Question 16 :
A wheel having angular momentum {tex}2\pi kg-m^2/s{/tex} about its vertical axis, rotates at the rate of {tex}60 {/tex}rpm about this axis, The torque which can stop the wheel's rotation in {tex}30{/tex} sec would be

Question 17 :
The moment of inertia of a circular disc of mass {tex} \mathrm { M } {/tex} and radius {tex} \mathrm { R } {/tex} about an axis passing through the centre of mass is {tex} \mathrm { I } _ { 0 } {/tex}. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is

Question 18 :
The moment of inertia of a body about a given axis is {tex} 1.2 \mathrm { kg } \mathrm { m } ^ { 2 } {/tex}. Initially, the body is at rest. In order to produce a rotational kinetic energy of {tex}1500{/tex} joule, an angular acceleration of {tex}25 \mathrm {radian/sec}^2{/tex} must be applied about that axis for a duration of

Question 19 :
A metal sheet {tex} 14 \mathrm { cm } \times 2 \mathrm { cm } {/tex} of uniform thickness is cut into two pieces of width {tex} 2 \mathrm { cm } . {/tex} The two pieces are joined and laid along {tex} X Y {/tex} plane as shown. The centre of mass has the coordinates<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0cb2ed6e36502132f2bd"><br>

Question 20 :
There is a flat uniform triangular plate {tex} A B C {/tex} such that {tex} A B = 4 \mathrm { cm } {/tex} {tex} B C = 3 \mathrm { cm } {/tex} and angle {tex} A B C = 90 ^ { \circ } {/tex} The moment of inertia of the plate about {tex} A B , B C {/tex} and {tex} C A {/tex} as axis is<br>respectively {tex} I _ { 1 } , I _ { 2 } {/tex} and {tex} I _ { 3 } . {/tex} Which one of the following is true?<br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f2f3d4faa335027dc790f' />

Question 21 :
Four identical thin rods each of mass {tex} M {/tex} and length {tex} l , {/tex} 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 :

Question 22 :
A solid cylinder of mass {tex} \mathrm { m } \ \& {/tex} radius {tex} \mathrm { R } {/tex} rolls down inclined plane without slipping. The speed of its {tex} \mathrm { C } . \mathrm { M } {/tex}. when it reaches the bottom is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0f0c6cde596850506e33bd"><br>

Question 23 :
A thin ring, a disk and an annular cylinder, of same mass {tex} M , {/tex} are released from a point {tex} 3.6 \mathrm { m } {/tex} from the ground up an inclined plane of {tex} 30 ^ { \circ } {/tex} degree inclination. The ring and the disk have the same radius {tex} R {/tex}. Times taken by the ring and disk to reach the ground are in the ratio,

Question 24 :
Consider a uniform square plate of side {tex} ^ { \prime } a ^ { \prime } {/tex} and mass {tex} ^ { \prime } M ^ { \prime } {/tex} . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is<br>

Question 25 :
Linear acceleration of cylinder of mass {tex} m _ { 2 } {/tex} is {tex} a _ { 2 } {/tex}. Then angular acceleration {tex} \alpha _ { 2 } {/tex} is (given that there is no slipping). <br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5e0f231b7d0c97188aace084.jpg" />

Question 26 :
If the angular momentum of a particle of mass {tex} m {/tex} rotating along a circular path of radius {tex} \mathrm { r } {/tex} with uniform speed is {tex} L , {/tex} the centripetal force acting on the particle is

Question 27 :
The moment of inertia of a uniform semicircular wire of mass {tex} \mathrm { m } {/tex} and radius {tex} \mathrm { r } {/tex}, about an axis passing through its centre of mass and perpendicular to its plane is {tex} \mathrm { mr } ^ { 2 } \left( 1 - \frac { \mathrm { k } } { \pi ^ { 2 } } \right) {/tex} then find the value of {tex} \mathrm { k } {/tex}.

Question 28 :
A bomb travelling in a parabolic path under gravity, explodes in mid air. The centre of mass of fragments will move

Question 29 :
A thick-walled hollow sphere has outside radius {tex} R _ { 0 } . {/tex} It rolls down an incline without slipping and its speed at the bottom is {tex} v _ { 0 } {/tex}. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be {tex} 5 v _ { 0 } / 4 {/tex}. The radius of gyration of the hollow sphere about an axis through its centre is

Question 30 :
The radius of a rotating disc is suddenly reduced to half without any change in its mass. Then its angular velocity will be