Work done by a frictional force is

On a pulley of mass $M$ hangs a rope with two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ tied at the ends as shown in the figure. The pulley rotates without any friction,whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley?

Three blocks with masses $m$,$2m$,and $3m$ are connected by strings,as shown in the figure. After an upward force $F$ is applied on block $m$,the masses move upward at a constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

$A$ spring is compressed between two blocks of masses $m_1$ and $m_2$ placed on a horizontal surface as shown in the figure. When the blocks are released,they have initial velocities $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest due to friction. The ratio $\left( \frac{x_1}{x_2} \right)$ is

Given $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$. How much distance in $cm$ will $m_2$ cover in $0.4 \, s$?

$A$ string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by