To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $\mathrm{R}_{\mathrm{E}}, \mathrm{g}=$ acceleration due to gravity on the surface of earth) :

(B) $\mathrm{mgR}_{\mathrm{E}}$

(A) $2 \mathrm{mgR}_{\mathrm{E}}$

(C) $\frac{1}{2} \mathrm{mgR}_{\mathrm{E}}$

(D) $4 \mathrm{mgR}_{\mathrm{E}}$

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Gravitation

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is

R_{E}, g =

acceleration due to gravity on the surface of earth) :

(A) $2 mgR_{E}$
(B) $mgR_{E}$ ✓ Correct
(C) $\frac{1}{2} mgR_{E}$
(D) $4 mgR_{E}$

Answer: (B)

Solution

The kinetic energy needed equals the magnitude of the gravitational potential energy at the surface:

K = \frac{GM m}{R _{E}}

.
Since

g = \frac{GM}{R _{E}^{2}}

, we have

GM = g R_{E}^{2}

, so

K = \frac{g R _{E}^{2} m}{R _{E}} = m g R_{E} .

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Single correct option

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