Question 2 :
A body executing uniform circular motion has find its position vector and acceleration vector:

Question 4 :
Consider the following two statements A and B&#160;and identify the correct choice.<br/>A) The moment of inertia of a rigid body is&#160;independent of its angular velocity.<br/>B) The radius of gyration of a rotating metallic&#160;disc is dependent on its temperature.<br/>

Question 5 :
Moment of inertia of a uniform horizontal solid cylinder of mass M about an axis passing through its edge and perpendicular to the axis of the cylinder when its length is 6 times its radius $'R'$ is:

Question 6 :
Consider the following two statements A and B&#160;and identify the correct choice:<br/>A) The rotational kinetic energy of a rolling body&#160;is always greater than its translational kinetic&#160;energy.<br/>B) The maximum value of radius of gyration of a&#160;rolling body cannot be greater than the radius of&#160;that body.<br/>

Question 7 :
A circular disc is rotating about its own axis at&#160;uniform rate completes $30$ rotations in one&#160;minute. The angular velocity of disc in rad $s^{-1}$ is:<br/>

Question 9 :
A fly-wheel is rotating about its own axis at an&#160;angular velocity $11\ rad/s$. Its angular velocity in&#160;revolution per minute ($rpm$) is:<br/>

Question 11 :
In the case of different rolling bodies match the ratio of rotational kinetic energy to the total kinetic energy<br><table class="wysiwyg-table"><tbody><tr><td>List - I</td><td>List - II</td></tr><tr><td>a) hollow sphere</td><td>e) $2 : 5$</td></tr><tr><td>b) solid cylinder</td><td>f) $1 : 2$</td></tr><tr><td>c) solid sphere </td><td>g) $1 : 3$</td></tr><tr><td>d) hollow cylinder </td><td>h) $2 : 7$</td></tr></tbody></table>

Question 12 :
Two particles A and B are moving with constant velocities $v_1={\hat{j}}$ and ${v_2}={2\hat{i}}$ respectively A is at co-ordinates $(0,0)$ and B is at $(-4,0)$.the angular velocity of B with respect to A at $t=2s$ is (all physical quantities are in SI units)

Question 13 :
lf $\vec{A}=-4\hat{i}+3\hat{j}$ and $\vec{B}=2\hat{i}+5\hat{j}$ and $\vec{C}=\vec{A}\times\vec{B}$ then $\vec{C}$ makes an angle of :<br/>

Question 15 :
The total angular momentum of a rigid body can be written as

Question 16 :
A slender uniform rod of mass $M$ and length $l$ is provided at one end so that it can rotate in a vertical plane$.$ There is negligible friction at the pivot$.$ The free end is held vertically above the pivot and then released$.$ The angular acceleration of the rod when it makes an angle $\theta $ with me

Question 17 :
A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter $1 &#160;m$. A mass of $2 &#160;kg$ is tied to the end of the cord and it is allowed to fall from rest. The weight falls $2 &#160;m$ in $4 &#160;s$. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is:(take $g=10 &#160;ms^{-2}$)&#160;<br/>

Question 18 :
A billiard ball of mass $m$ and radius $r$, when hit in a horizontal direction by a cue at a height $h$ above its centre, acquired a linear velocity ${ v }_{ 0 }$. The angular velocity ${ \omega }_{ 0 }$ acquired by the ball is

Question 19 :
The kinetic energy $T$ of a particle moving along a&#160;circle of radius $R$ depends on the distance covered&#160;as $T=as^{2}$. The force acting on the&#160;particle is:<br/>

Question 20 :
A solid cylinder is placed on the end of an inclined plane. It is found that the plane can be tipped at an angle $\theta$ before the cylinder starts to slide. When the cylinder turns on its sides and is allowed to roll, it is found that the steepest angle at which the cylinder performs pure rolling is $\phi$. The ratio $tan\phi : tan\theta$ is: