Question

Mass of a planet is $5\times {10}^{24}$ kg and radius is $6.1\times {10}^6$m. The energy needed to send a $2$ kg body into space from its surface, would be.

• A. $9$ joule
• B. $18$ joule
• C. $2.2\times {10}^8$joule
• D. $1.1\times {10}^8$joule

Answer 1

Answer: (D)

$1.1\times {10}^8$joule

Energy required to send a body into the space from the surface of planet is equal to the negative of potential energy at surface.

At surface $P.E=-\frac{GMm}{R}$

Thus energy required $E=\frac{GMm}{R}$

Given: $M=5\times {10}^{24}kgm=2kgR=6.1\times {10}^{6}mG=6.67\times {10}^{-11}N{m}^2/k{g}^2$

$⟹E=1.1\times {10}^{8}Joule$