Two blocks $A$ and $B$,each of the same mass,are attached by a thin inextensible string through an ideal pulley. Initially,block $B$ is held in position as shown in the figure. Now,block $B$ is released. Block $A$ will slide to the right and hit the pulley in time $t_A$. Block $B$ will swing and hit the surface in time $t_B$. Assume the surface is frictionless. [Hint: Tension $T$ in the string acting on both blocks is the same in magnitude. Acceleration needed for horizontal motion is provided by $T$.]

The maximum acceleration with which a body of mass $200 \, kg$ is lowered into a well using a rope having a breaking force of $50 \, kg$-wt is (Acceleration due to gravity $= 10 \, ms^{-2}$) (in $ \, ms^{-2}$)

Two masses $m_1 = 5\, kg$ and $m_2 = 4.8\, kg$ tied to a string are hanging over a light frictionless pulley. The acceleration of the masses when they are free to move is $...........\, m/s^2$. $(g = 9.8\, m/s^2)$

Consider a body of mass $3\,kg$ at rest on a smooth horizontal table. This body is connected by a light string,which passes over a smooth pulley at the edge of the table,to another body of mass $2\,kg$ hanging freely. This $2\,kg$ mass is released from rest. Now consider the following statements:
$(A)$ The masses remain at rest.
$(B)$ The $3\,kg$ mass moves uniformly while the $2\,kg$ mass moves with acceleration $\frac{2}{5}g\,m/s^2$.
$(C)$ Both bodies move with acceleration $\frac{2}{5}g\,m/s^2$.
$(D)$ The tension in the string near the first body is more than that near the second body.
$(E)$ The tension in the string is $\frac{6g}{5}\,N$.
Then the correct statements are:

$A$ pendulum bob of mass $50 \,g$ is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately .......... $N$.

$A$ lift is tied with thick iron ropes having mass $M$. The maximum acceleration of the lift is $a \ m/s^2$ and the maximum safe stress is $S \ N/m^2$. The minimum diameter of the rope is