An object of uniform density rolls up the curved path with the initial velocity $v_{\mathrm{o}}$ as shown in the figure. If the maximum height attained by an object is $\frac{7 v_0^2}{10 \mathrm{~g}}$ ( $\mathrm{g}=$ acceleration due to gravity), the object is a $\_\_\_\_$ .

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $\left(R_e\right)$. The increase in potential energy will be $\_\_\_\_$ .

( $g$ is acceleration due to gravity at the surface of earth)

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is $\_\_\_\_$ - ( $S$ is the surface tension of mercury).

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $P T^3=$ constant. The coefficient of volume expansion of the gas is $\_\_\_\_$ .