Question

Mass of a planet is $5\times {10}^{24}$kg nd radius is $6.1\times {10}^6$m. The energy needed to send a 2kg body from its surface in space is -

• A. $9J$
• B. $10J$
• C. $2.2\times {10}^{8}J$
• D. $1.1\times {10}^{8}J$

Answer 1

The correct option is D $1.1\times {10}^{8}J$

Given,

$m=2kg$

$M=5\times {10}^{24}kg$

$G=6.7\times {10}^{-11}N{m}^2/k{g}^2$

$r=6.1\times {10}^{6}m$

The energy needed to send a 2kg body from the surface is equal to gravitational potential energy,

$E=\frac{GMm}{r}$

$E=\frac{6.7\times {10}^{-11}\times 2\times 5\times {10}^{24}}{6.1\times {10}^6}$

$E=1.1\times {10}^{8}J$

The correct option is D.