A disc is rotating with an angular velocity $\omega_0$. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes $\frac{{{\omega _0}}}{2}$ after $n$ rotations. How many more rotations will it make before coming to rest
$n$
$2n$
$\frac{n}{2}$
$\frac{n}{3}$
The centre of mass of two masses $m$ and $m'$ moves by distance $\frac {x}{5}$ when mass $m$ is moved by distance $x$ and $m'$ is kept fixed. The ratio $\frac {m'}{m}$ is
A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega $. Its centre of mass rises to a maximum height of:
A plank is moving in a horizontal direction with a constant acceleration $\alpha \hat{ i }$. A uniform rough cubical block of side $l$ rests on the plank and is at rest relative to the plank. Let the centre of mass of the block be at $(0, l / 2)$ at a given instant. If $\alpha =g / 10$, then the normal reaction exerted by the plank on the block at that instant acts at
Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring $= m$, radius $= r$ )
An ant is sitting at the edge of a rotating disc. If the ant reaches the other end, after moving along the diameter, the angular velocity of the disc will