$A$ man slides down a light rope whose breaking strength is $\eta$ times the weight of the man $(\eta < 1)$. What is the maximum acceleration of the man so that the rope does not break?

Two bodies of masses $10\; kg$ and $20\; kg$ respectively,kept on a smooth horizontal surface,are tied to the ends of a light string. $A$ horizontal force $F = 600\; N$ is applied to $(i)\; A$,$(ii)\; B$ along the direction of the string. What is the tension in the string in each case?

$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

Three blocks of masses $m$, $2m$, and $3m$ are pushed with a force $F$ across a frictionless table as shown in the figure. Let $N_{1}$ be the contact force between the left two blocks ($m$ and $2m$) and $N_{2}$ be the contact force between the right two blocks ($2m$ and $3m$). Then:

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:

$A$ monkey is descending from the branch of a tree with constant acceleration. If the breaking strength of the branch is $75 \%$ of the weight of the monkey,what is the minimum acceleration with which the monkey can slide down without breaking the branch?