Question 1 :
A flywheel rotates at a constant speed of $3000\ rpm$. The angle described by the shaft in radian in one second is:<br/>

Question 2 :
The centre of gravity of an object is ______ whether it is placed near the surface of the Earth or near the surface of the Moon.

Question 3 :
What is the position of centre of gravity of a cylinder?<br/>

Question 4 :
A motor cyclist takes a U-turn in $4$ seconds. His angular velocity will be _______ $rads^{-1}$.<br/>

Question 6 :
For a bowling ball, how far apart are the center of gravity and center of mass?<br>

Question 7 :
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 8 :
A dancer is rotating on smooth horizontal floor with an angular momentum $L$. The dancer folds her hands so that her momentof inertia decreases by $25$%. The new angular momentum is.<br>

Question 9 :
<p class="wysiwyg-text-align-left">If $A = 5$ units, $B = 6$ units and&#160;$|\vec{A}\times\vec{B}|=15$ units, then the angle between&#160; $\vec{A}$ and $\vec{B}$ is:</p><p class="wysiwyg-text-align-left"></p><p class="wysiwyg-text-align-left"></p>

Question 10 :
Find out the instantaneous velocity of a point on the outer edge of a circular plate with a diameter of $4 m$ rotating at $120$&#160;revolutions per minute.

Question 11 :
An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver?<br>

Question 12 :
A scooter is going round a circular track with a speed of 30 $ms^{-1}$. The radius of the circular track is 50 m. The angular velocity of the scooter is<br>

Question 13 :
A flywheel making $120$ r.p.m is acted upon by&#160;a retarding torque producing angular retardation&#160;of $\pi &#160;\ rad/s^{2}$. Time taken by it to come to rest is:<br/>

Question 14 :
The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then, its radius of gyration about a parallel axis through its centre of mass will be :

Question 15 :
A torque of $0.5 &#160;Nm$ is required to drive a screw into a&#160;wooden frame with the help of a screw driver. If&#160;one of the two forces of couple produced by screw&#160;driver is $50 &#160;N$, the width of the screw driver is:<br/>

Question 16 :
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 17 :
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 18 :
What is the ratio of the linear speeds for the tips of hour and minute hands of a clock if the minute hand is $2.5$ times longer than the hour hand?

Question 19 :
The velocity of a car travelling on a straight road is $36 kmh^{-1}$ at an instant of time. Now travelling with uniform acceleration for 10 s, the velocity becomes exactly double. If the wheel radius of the car is 25 cm, then which of the following numbers is the closest to the number of revolutions that the wheel makes during this 10 s?

Question 20 :
A grinding wheel attained a velocity of $20\ rad/sec$ in $5\ sec$ starting from rest. Find the number of revolutions made by the wheel.