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…
JEE Main 2026 — Physics Mechanics
2026mcqmedium
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/s2)
Official previous-year question
Held on 2 Apr 2026 · Verified 6 Jul 2026.
Options
A
11.2 km/s; 6.27×107 J
B
11.2 km/s; 12.54×107 J
C
8.8 km/s; 6.27×107 J
D
8.8 km/s; 12.54×107 J
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Solution
By conservation of mechanical energy, the total energy of the body at infinity is zero.
When the body reaches the surface of the earth, its potential energy is −RGMm and kinetic energy is k=21mv2.
0=k−RGMm
k=RGMm=mgR
Substituting m=1 kg, g=9.8 m/s2, and R=6400×103 m:
k=1×9.8×6400×103=6.272×107 J
The velocity v is given by 21mv2=k.
v=2gR=2×9.8×6400×103
v=125.44×106=11.2×103 m/s =11.2 km/s
Answer: 11.2 km/s; 6.27×107 J
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