Two objects $A$ and $B$,each of mass $m$,are connected by a light inextensible string. They are restricted to move on a frictionless ring of radius $R$ in a vertical plane (as shown in the figure). The objects are released from rest at the position shown. Then,the tension in the cord just after release is

If a ship of mass $4 \times 10^{7} \,kg$ initially at rest is pulled by a force of $5 \times 10^{4} \,N$ through a distance of $4 \,m$, then the speed of the ship will be (resistance due to water is negligible). (in $\,ms^{-1}$)

The arrangement of a two-block system is as shown. Assuming the surfaces to be frictionless,the net force acting on the $1 \, kg$ and $2 \, kg$ blocks are,respectively:

Three blocks of masses $4 \ kg$, $2 \ kg$, and $1 \ kg$ respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \ N$ is applied on the $4 \ kg$ block, the contact force between the $4 \ kg$ and the $2 \ kg$ block will be: (in $N$)

$A$ block of mass $m$ slides down on a wedge of mass $M$ as shown in the figure. Let $\vec a_1$ be the acceleration of the wedge and $\vec a_2$ be the acceleration of the block with respect to the ground. $N_1$ is the normal reaction between the block and the wedge,and $N_2$ is the normal reaction between the wedge and the ground. Friction is absent everywhere. Select the incorrect alternative.

Two bodies $A$ and $B$ of masses $10\, kg$ and $15\, kg$ respectively,kept on a smooth horizontal surface,are tied to the ends of a light string. If $T$ represents the tension in the string when a horizontal force $F = 500\, N$ is applied to $A$ (as shown in figure $I$) and $T'$ is the tension when it is applied to $B$ (figure $II$),then which of the following is true?