$A$ truck is moving at a speed of $54 \ km/h$. The radius of its wheels is $50 \ cm$. If the wheels come to rest after $20$ rotations upon applying brakes,what is the linear distance covered by the truck during this time? What is the angular acceleration of the wheels?

$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

$A$ rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha - \beta t$,where $t$ is time and $\alpha, \beta$ are constants. Find the angle (in radians) through which it rotates before it stops.

$A$ door $1.6 \,m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4 \,m$ distance from the hinges for opening or closing the door is (in $\,N$)

How can one verify that an object is undergoing rotation about a fixed axis?

$A$ rod of length $l$ and mass $m$ lies on a fixed horizontal smooth table. $A$ cord is led through a pulley,and its horizontal part is attached to one end of the rod,while its vertical part is attached to a block of mass $m_1$. Assume the pulley and the cord are ideal. The maximum possible acceleration of the rod's centre of mass $C$ (for all possible values of masses $m$ and $m_1$) at the moment of releasing the block $m_1$ is $\frac{g}{n}$. Find the value of $n$.