JEE Main20262 April 2026Evening ShiftPhysicsGravitationActual
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 )
Options
- A11.2 km/s; 6.27 10^7 J
- B11.2 km/s; 12.54 10^7 J
- C8.8 km/s; 6.27 10^7 J
- D8.8 km/s; 12.54 10^7 J
Correct answer
A. 11.2 km/s; 6.27 10^7 J
Step-by-step 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 - GMm R and kinetic energy is k = 1 2 mv^2 . 0 = k - GMm R k = GMm R = mgR Substituting m = 1 kg, g = 9.8 m/s ^2 , and R = 6400 10^3 m: k = 1 9.8 6400 10^3 = 6.272 10^7 J The velocity v is given by 1 2 mv^2 = k . v = 2gR = 2 9.8 6400 10^3 v = 125.44 10^6 = 11.2 10^3 m/s = 11.2 km/s Answer: 11.2 km/s; 6.27 10^7 J