A thin uniform annular disc (see figure) of mass $M$ has outer radius $4R$ and inner radius $3R$. The work required to take a unit mass from point $P$ on its axis to infinity is: 

A rocket is launched normal to the surface of the Earth away from the Sun along the line joining the Sun and the Earth. The Sun is $3\times {10}^5$ times heavier than the Earth and is at a distance $2.5\times {10}^4$ times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is ${\mathrm{v}}_{\mathrm{e}}=11.2 \mathrm{km} {\mathrm{s}}^{–1}.$ The minimum initial velocity $\left(v_{\mathrm{s}}\right)$ required for the rocket to be able to leave the Sun-Earth system is closest to : (Ignore the rotation and revolution of the Earth and the presence of any other planet)

A planet of mass $M$ has two natural satellites with masses $m_1$and $m2$. The radii of their circular orbits are $R_1$ and $R_2$, respectively. Ignore the gravitational force between the satellites. Define $v_1, L_1, K_1 \mathrm{and} T_1$ to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite $1$ and $v_2, L_2, K_{2 }\mathrm{and} T_2$ to be the corresponding quantities of satellite $2$. Given $m_1/m_{2 }= 2$ and $R_1/R_2 = 1/4,$ match the ratios in List-I to the numbers in List-II.