JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Gravitation

WhatsApp Email

If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____.
(Take radius of earth to be 6400 km and

g = 9.8 m / s^{2}

)

(A) $11.2 km / s; 6.27 \times 1 0^{7} J$ ✓ Correct
(B) $11.2 km / s; 12.54 \times 1 0^{7} J$
(C) $8.8 km / s; 6.27 \times 1 0^{7} J$
(D) $8.8 km / s; 12.54 \times 1 0^{7} J$

Answer: (A)

Solution

A body falling from infinity reaches the surface with the escape speed, found from energy conservation

\frac{1}{2} m v^{2} = \frac{GM m}{R _{e}}

, i.e.

v = \frac{2 GM}{R _{e}} = 2 g R_{e}

. Thus

v = 2 \times 9.8 \times 6400 \times 1 0^{3} = 1.12 \times 1 0^{4} m/s = 11.2 km/s

. The kinetic energy gained is

k = \frac{1}{2} m v^{2} = \frac{1}{2} \times 1 \times (11200)^{2} = 6.27 \times 1 0^{7} J

. The body arrives with speed

11.2

km/s and kinetic energy

6.27 \times 1 0^{7}

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Gravitation →

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Gravitation

Solution

More JEE Main questions on Gravitation