A body of mass m is situated at a distance 4R above the earth's surface, where R is the radius of earth. How much minimum energy be given to the body so that it may escape

Q. The kinetic energy needed to project a body of mass m from the earth' surface to infinity is
(a)

\frac{1}{4} m g R

(b)

\frac{1}{2} m g R

(c)

m g R

(d)

2 m g R

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The radius of the earth is R and acceleration due to gravity at its surface is 'g'. If a body of mass 'm' is sent to a height of R/4 from the earth's surface, the potential energy is:

The correct option is C 4mgR/5We know that,g=GMR2u=GMm(R+R4)⇒u=4GMm5Ru=4GMm5R⇒u=4mgR5Then,Option C is correct answer.

The radius of the earth is $R$ and acceleration due to gravity at its surface is ' $g$ '. If a body of mass ' $m$ ' is sent to a height of $R / 4$ from the earth's surface, the potential energy is:

The correct option is C $4 m g R / 5$
We know that,

$\begin{matrix} g = \frac{G M}{R^{2}} u = \frac{G M m}{(R + \frac{R}{4})} \Rightarrow u = \frac{4 G M m}{5 R} u = \frac{4 G M m}{5 R} \end{matrix}$

$\Rightarrow u = \frac{4 m g R}{5}$
Then,
Option $C$ is correct answer.