The same spring is attached to $2 \ kg, 3 \ kg$ and $1 \ kg$ blocks in three different cases as shown in the figure. If $x_1, x_2$ and $x_3$ are the extensions in the spring in these cases,respectively,find the correct relation between them.

$A$ 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 .......... $N$.

One end of a massless rope,which passes over a massless and frictionless pulley $P$,is tied to a hook while the other is free. The maximum tension the rope can bear is $360 \ N$. With what value of maximum safe acceleration (in $m \ s^{-2}$) can a man of $60 \ kg$ climb on the rope?

For the system shown in the figure,$m_1 > m_2 > m_3 > m_4$. Initially,the system is at rest in equilibrium. If the string joining $m_4$ and the ground is cut,then just after the string is cut:
Statement $I$: $m_1$,$m_2$,and $m_3$ remain stationary.
Statement $II$: The value of acceleration of all the $4$ blocks can be determined.
Statement $III$: Only $m_4$ remains stationary.
Statement $IV$: Only $m_4$ accelerates.
Statement $V$: All the four blocks remain stationary.
Now,choose the correct option.

In the case of a wire having negligible mass,suspended from a ceiling and stretched under the action of a weight $F$ suspended from its other end,the tension at any cross-section of the wire is

Two masses of $5 \ kg$ and $10 \ kg$ are suspended from a massless pulley as shown in the figure. Calculate the acceleration of the system when the masses are left free.