A nucleus disintegrates into two nuclear parts which have their velocities in the ratio \(2:1\). The ratio of their nuclear size will be:
1. \( 2^{1 / 3}: 1 \)
2. \( 1: 3^{1 / 2} \)
3. \( 3^{1 / 2}: 1 \)
4. \( 1: 2^{1 / 3}\)

A rod Ab of length 1 is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end B is 2 m/s towards the negative direction of x. The speed of end A will be:
       

1.  $\sqrt{3}{\mathrm{ms}}^{-1}$

2.  $\frac{2}{\sqrt{3}}{\mathrm{ms}}^{-1}$

3.  $\sqrt{2}{\mathrm{ms}}^{-1}$

4.  $\frac{\sqrt{5}}{2}{\mathrm{ms}}^{-1}$

A slab consists of portions of different materials of the same thickness and having the conductivities K₁ and K₂. The equivalent thermal conductivity of the slab is:

1.  ${\mathrm{K}}_1+{\mathrm{K}}_2$

2.  $\sqrt{{\mathrm{K}}_1+{\mathrm{K}}_2}$

3.  $\frac{2{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}$

4.  $\sqrt{\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}}$

Two rigid boxes containing different ideal gases are placed on the table. Box \(A\) contains one mole of nitrogen at temperature \(T_0\), while box \(B\) contains \(1\) mole of helium at temperature \(\frac{7T_0}{3}\). The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes) then the final temperature of gases, \(T_f\) in terms of \(T_0\) is:
1. \( \frac{2 \mathrm{~T}_0}{5} \)
2. \( \frac{3 \mathrm{~T}_0}{7} \)
3. \( \frac{5 \mathrm{~T}_0}{3} \)
4. \( \frac{9 \mathrm{~T}_0}{7}\)