Initially a satellite of 100 kg is in a circular orbit of radius $1.5 \mathrm{R}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3 R_E$ by supplying $\alpha \times 10^6 \mathrm{~J}$ of energy The value of $\alpha$ is $\_\_\_\_$ .

(Take Radius of Earth $R_E=6 \times 10^6 \mathrm{~m}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm{C}$ to $87^{\circ} \mathrm{C}$. The rate of consumption of the gas is $\_\_\_\_$ $\mathrm{g} / \mathrm{s}$.

(Take heat of combustion of gas $=5.0 \times 10^4 \mathrm{~J} / \mathrm{g}$ ) specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$

Potential energy ( $V$ ) versus distance ( $x$ ) is given by the graph. Rank various regions as per the magnitudes of the force ( $F$ ) acting on a particle from high to low.

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is $\_\_\_\_$ m. (Atomic number of gold $=79$ and $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9$ in SI units)