"The value of the escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet." Is this statement correct? If not,correct it.

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Value of escape velocity on the surface of the Earth	$(a)$ $2.38 \, km \, s^{-1}$
$(2)$ Value of escape velocity on the surface of the Moon	$(b)$ $7.92 \, km \, s^{-1}$
	$(c)$ $11.2 \, km \, s^{-1}$

$A$ very small groove is made in the earth,and a particle of mass $m_0$ is placed at $\frac{R}{2}$ distance from the centre. Find the escape speed of the particle from that place.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: The kinetic energy needed to project a body of mass $m$ from the Earth's surface to infinity is $\frac{1}{2} mgR$,where $R$ is the radius of the Earth.
Reason $R$: The maximum potential energy of a body is zero when it is projected to infinity from the Earth's surface.
In the light of the above statements,choose the correct answer from the options given below.

The escape velocity of a rocket launched from the surface of the earth:

Masses and radii of Earth and Moon are $M_1, M_2$ and $R_1, R_2$ respectively. The distance between their centers is $d$. The minimum velocity given to a mass $m$ from the midpoint of the line joining their centers so that it escapes the gravitational field of both is: