An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g =10 ms -2 and radius of earth =6400 km ]

Question

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g =10 ms -2 and radius of earth =6400 km ] (A) 48 MJ (B) 24 MJ (C) 36 MJ (D) 12 MJ

Tardigrade Admin · Accepted Answer

U i =(- GMm / R ) U f =-( GMm /4 R ) Δ U = U f - U i =(3 GMm /4 R ) =(3/4) mgR =(3/4) × 1 × 10 × 64 × 105 =48 MJ

Q. An object of mass $1 k g$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $g = 10 m s^{- 2}$ and radius of earth $= 6400 km$ ]

$48 M J$

$24 M J$

$36 M J$

$12 M J$

$U_{i} = \frac{- GM m}{R}$
$U_{f} = - \frac{GM m}{4 R}$
$Δ U = U_{f} - U_{i} = \frac{3 GM m}{4 R}$
$= \frac{3}{4} m g R$
$= \frac{3}{4} \times 1 \times 10 \times 64 \times 1 0^{5}$
$= 48 M J$

Q. An object of mass 1kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g=10ms−2 and radius of earth =6400km ]

48MJ

24MJ

36MJ

12MJ