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

$A$ car of mass $1250 \ kg$ is moving at $30 \ m/s$. Its engine delivers $30 \ kW$ while the resistive force due to the surface is $750 \ N$. What is the maximum acceleration that can be given to the car in $m/s^2$?

$A$ block of mass $m$ slides on a wooden wedge,which in turn slides backward on a horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg, M = 16 \, kg$. Assume all surfaces shown in the figure to be frictionless.

$A$ force $F = 10t$ acts on a block of mass $10 \, kg$ as shown in the figure. Find the time $t$ when the block loses contact with the surface.

$A$ chain is lying on an absolutely smooth table,with half of it hanging over the edge of the table as shown in figure $(a)$. The time it takes to slip off the table is affected if two equal weights are attached,one to each end as shown in figure $(b)$.
$t_a$ : time taken to slip in situation $(a)$
$t_b$ : time taken to slip in situation $(b)$

$A$ 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.