If 1000 droplets of water of surface tension $$0.07 \mathrm{~N} / \mathrm{m}$$, having same radius $$1 \mathrm{~mm}$$ each, combine to from a single drop. In the process the released surface energy is :-

$$\left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)$$

As shown in figure, a $$70 \mathrm{~kg}$$ garden roller is pushed with a force of $$\vec{F}=200 \mathrm{~N}$$ at an angle of $$30^{\circ}$$ with horizontal. The normal reaction on the roller is

(Given $$\mathrm{g=10~m~s^{-2}}$$)

The pressure of a gas changes linearly with volume from $$\mathrm{A}$$ to $$\mathrm{B}$$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

The correct relation between $$\gamma = {{{c_p}} \over {{c_v}}}$$ and temperature T is :