Question 2 :
A circular disc is rotating about its own axis at uniform rate completes $30$ rotations in one minute. The angular velocity of disc in rad $s^{-1}$ is:<br/>
Question 3 :
A sparrow flies around a circular path at a constant speed. If the radius of the circular path is 15.0 m and the sparrow takes 10 seconds to complete one lap. how fast is the sparrow flying?
Question 4 :
A motor cyclist takes a U-turn in $4$ seconds. His angular velocity will be _______ $rads^{-1}$.<br/>
Question 5 :
A solid cylinder, a solid sphere and a hollow sphere each of mass m and radius r are released from the top of a smooth inclined plane. Then which of the bodies has minimum acceleration down the plane?
Question 6 :
A catapult with a basket of mass 50 kg launches a 200 kg rock by swinging around from a horizontal to a vertical position with an angular velocity of 2.0 rad/s. Assuming the rest of the catapult is massless and the catapult arm is 10 m long, what is the velocity of the rock as it leaves the catapult?<br>
Question 7 :
The angular velocity ($\omega$ of a particle is related to the linear velocity$v$ of the particle moving in a circular motion or radius R using the formula
Question 8 :
A particle moves along a circular path of radius $r$ with uniform speed $v$. The angle described by the particle in one second is given by:<br/>
Question 10 :
Consider the following two statements A and B and identify the correct choice:<br/>A) The rotational kinetic energy of a rolling body is always greater than its translational kinetic energy.<br/>B) The maximum value of radius of gyration of a rolling body cannot be greater than the radius of that body.<br/>
Question 11 :
The instantaneous velocity of a point on the outer edge of a disk with a diameter of 4 m that is rotating at 120 revolutions per minute is most nearly:
Question 12 :
Which of the following is true about the angular momentum of a cylinder down a slope without slipping?
Question 13 :
For the same mass which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?
Question 14 :
State whether true or false.<br/>A couple can never be replaced by a single force.
Question 15 :
$ \xrightarrow [ A ]{ } .\left( \xrightarrow [ A ]{ } \times \xrightarrow [ B ]{ } \right) $
Question 16 :
Let $a = 2 \widehat i + \widehat j - 2 \widehat k$ and $b = \widehat i + \widehat j$. If c is a vector such that $a . c = |c|, |c - a| = 2 \sqrt 2$ and the angle between $a \times b$ and c is $30^o$. Then, $[(a \times b) \times c]$ is equal to
Question 18 :
Three masses are placed on the x-axis: $300g$ at origin, $500g$ at $x=40cm$ and $400g$ at $x=70cm$. The distance of the centre of mass from the origin is-
Question 19 :
If $b$ and $c$ are any two non-collinear vectors, and $a$ is any vector, then<br>$\left( a\cdot b \right) b+\left( a\cdot c \right) c+\cfrac { a\cdot \left( b\times c \right) }{ { \left| b\times c \right| }^{ 2 } } \left( b\times c \right) $ is equal to
Question 20 :
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal track. If the  child starts running towards the other end of the trolley with a speed $u$. The centre of mass of the system (trolley+child) will move with a speed:
Question 21 :
All the particles of a body are situated at a distance $R$ from the origin. The distance of centre of mass of the body from the origin is
Question 22 :
If the vectors $(\hat i+\hat j+\hat k)$ and $3\hat i$ form two sides of a triangle, then area of the triangle is:
Question 23 :
Assertion: A hollow shaft is found to be stronger than a solid shaft made of same material.
Reason: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.
Question 24 :
A torque of $100\ N-m$ acting on a wheel at rest, rotates it through $200$ radian in $10s$. what is the moment of inertia of the wheel?
Question 25 :
A solid cylinder rolls down an inclined plane. Its mass is $2  kg$ and radius $0.1  \ m$. If the height of the inclined plane is $4  m$, its rotational kinetic energy, when it reaches the foot of the plane is:<br/>
Question 26 :
Masses 8, 2, 4, 2 kg are placed at the corners A, B, C, D respectively of a square ABCD of diagonal $80\ cm$. The distance of center of mass from A is:<br/>
