A mass $2m$ rests on a horizontal table. It is attached to a light inextensible string which passes over a smooth pulley and carries a mass $m$ at the other end. If the mass $m$ is raised vertically to a height $h$ and is then dropped, what is the speed with which the mass $2m$ begins to rise?

Q. An inextensible string is passing over a light frictionless pulley. One end of the string is connected to a block of mass $4m$ which is resting on a horizontal surface. To another end, a plate of mass $m$ is attached and is hanging in the air. A particle of mass $m$ strikes from above with vertical velocity $v_0$ and sticks to the plate. Calculate maximum height attained by the block of mass $4m$.

Q. A string with one end fixed on a rigid well passing over a fixed frictionless pulley at a distance of $2m$ from the wall, has a point mass $M=2kg$ attached to it at a distance of $1m$, from the wall. A mass $m=0.5kg$ attached at the free end is held at rest so that the string is horizontal between the wall and the pulley, and vertical beyond the pulley. If the speed with which the mass $M$ will hit the wall when mass $m$ released is $335\times {10}^{-k}$, then $k$ is

Q. A mass of $2kg$ hangs freely at the end of a string, which passes over a smooth pulley fixed at the edge of a smooth table. The other end of the string is attached to a mass $M$ on the table. If the mass on the table is doubled the tension in the string increases by one-half. The mass $M$ is :

Q. Two masses, (M+m) and (M-m) are attached to the ends of a light inextensible string and the string is made to pass over the surface of a smooth fixed pulley. When the masses are released from rest, the acceleration of the system is

Q. A string with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass $M=2\text{kg}$ attached to it at a distance of 1 m from the wall. A mass $m=0.5\text{kg}$ attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed in m/s upto 1 decimal place with which the mass $M$ will hit the wall when the mass m is released and $g=9.8{\text{ms}}^{-2}$?