A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy of the system is '$$K$$'. The child now stretches his arms so that the moment of inertia of the system becomes double. The kinetic energy of the system now is

If the pressure of an ideal gas is decreased by $$10 \%$$ isothermally, then its volume will

The critical angle for light going from medium '$$x$$' to medium '$$Y$$' is $$\theta$$. The speed of light in medium '$$x$$' is '$$V$$' . The speed of light in medium '$$Y$$' is

A needle is $$7 \mathrm{~cm}$$ long. Assuming that the needle is not wetted by water, what is the weight of the needle, so that it floats on water?

$$\left[\mathrm{T}=\right.$$ surface tension of water $$\left.=70 \frac{\mathrm{dyne}}{\mathrm{cm}}\right]$$

[acceleration due to gravity $$=980 \mathrm{~cm} \mathrm{~s}^{-2}$$]