The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02 \%$$ is _______ $$m$$.
(Take density of sea water $$=10^3 \mathrm{kgm}^{-3}$$, Bulk modulus of rubber $$=9 \times 10^8 \mathrm{~Nm}^{-2}$$, and $$g=10 \mathrm{~ms}^{-2}$$)
A body starts falling freely from height $$H$$ hits an inclined plane in its path at height $$h$$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $$\frac{H}{h}$$ for which the body will take the maximum time to reach the ground is __________.
A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{2 A}{3}$$. The new amplitude of motion is $$\frac{n A}{3}$$. The value of $$n$$ is ___________.
The mass defect in a particular reaction is $$0.4 \mathrm{~g}$$. The amount of energy liberated is $$n \times 10^7 \mathrm{~kWh}$$, where $$n=$$ __________. (speed of light $$\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$$