$A$ $2 ~kg$ ball moving at $24 ~ms^{-1}$ undergoes an inelastic head-on collision with a $4 ~kg$ ball moving in the opposite direction at $48 ~ms^{-1}$. If the coefficient of restitution is $2/3$,what are their velocities in $ms^{-1}$ after the impact?

Select the correct statement from the following.

When one end of a capillary tube is dipped in water,the height of the water column is $h$. The upward force of $105 \text{ dyne}$ due to surface tension is balanced by the force due to the weight of the water column. What is the inner circumference of the capillary (in $\text{ cm}$)? (Surface tension of water $= 7 \times 10^{-2} \text{ N m}^{-1}$)

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

The spring balance $A$ reads $2 \ kg$ with a block $m$ suspended from it. $A$ balance $B$ reads $5 \ kg$ when a beaker with liquid is placed on the pan of the balance. The two balances are now arranged such that the hanging mass is inside the liquid in the beaker as shown in the figure. In this situation:

$A$ fresh radioactive sample is given at $t = 0$. Its decay fraction is $\frac{1}{5}$ at $t_1$ instant and $\frac{4}{5}$ at $t_2$ instant. Its mean life is