A mass $m$ hangs with the help of a string wrapped around a pulley on a firctionless  bearing. The pulley has mass $m$ and radius $R$. Assuming pulley to be a perfect  uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the  pulley, is:-

A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

[The coefficient of static friction, $\mu_{ s },$ is $\left.0.4\right]$

A horizontal heavy uniform bar of weight $W$ is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to

In a physical balance working on the principle of moments, when $5\, mg$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

A ring is formed by joining two uniform semi circular rings $ABC$ and $ADC$. Mass of $ABC$ is thrice of that of $ADC$. If the ring is hinged to a fixed support ,at $A$, it can rotate freely in a vertical plane. Find the value of $tan\,\theta$, where $\theta$ is the angle made. by the line $AC$ with the vertical in equilibrium

As shown in figure, a mass $m$ = $500\  g$ hangs from the rim of a wheel of radius $r$ = $20\  cm$. When released from rest, the mass falls $2.0\  m$ in $8\  sec$. Then moment of inertia of the wheel is.......... $kg-m^2$. $(g = 10\  m/s^2)$