In free space,a shell moving with velocity $60\,m/s$ along the positive $x$-axis explodes into two pieces of mass ratio $1:2$ when it passes through the origin. After the explosion,the velocity of the centre of mass is ........ $m/s$.

Two spheres of the same material have radii $1\ m$ and $4\ m$ and temperatures $4000\ K$ and $2000\ K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

The current flowing through an inductor of self-inductance $L$ is continuously increasing at a constant rate. The variation of induced e.m.f. $(e)$ versus $dI/dt$ is shown graphically by which graph?

What is the equivalent capacitance of the system of capacitors between $A$ and $B$?

$A$ block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

Three moles of an ideal monoatomic gas undergo a cyclic process as shown in the figure. The temperatures of the gas in different states marked as $1, 2, 3$ and $4$ are $400 \ K, 700 \ K, 2500 \ K$ and $1100 \ K$ respectively. The work done by the gas during the process $1-2-3-4-1$ is (universal gas constant is $R$): (in $R$)