Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface. The acceleration of mass $m$ is:

For the given system, what is the strain in wire $W_1$? Assume the wire $W_1$ connects the two blocks on the table, and wire $W_2$ connects the second block to the hanging mass.

$A$ monkey of mass $m$ is climbing a rope hanging from the roof with acceleration $a$. The coefficient of static friction between the body of the monkey and the rope is $\mu$. Find the direction and value of the friction force on the monkey.

Three blocks of different masses connected with inextensible strings are pulled by a force $F$ on a frictionless surface as shown in the figure. The ratio of tensions $T_1$ to $T_2$ is

$A$ small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mkv^{2}$ where $v$ is its speed. The maximum height attained by the ball is

$A$ monkey of mass $20\,kg$ is holding a vertical rope. The rope will not break when a mass of $25\,kg$ is suspended from it but will break if the mass exceeds $25\,kg$. What is the maximum acceleration with which the monkey can climb up along the rope in $m/s^2$? (Take $g = 10\,m/s^2$)