Q. If the diameter of mass is 6760 km and mass one-tenth that of earth. The diameter of earth is 12742 km. If acceleration due to gravity on earth is ${9.8\ ms}^{- 2},$ the acceleration due to gravity on mass is
A) ${34.8\ ms}^{- 2}$
B) ${2.48\ ms}^{- 2}$
C) $3.48\ {ms}^{- 2}$
D) $28.4{\ ms}^{- 2}$
Explanation
(c) $Acceleration\ due\ to\ gravity,\ g = \frac{GM}{R^{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{M}}{g_{E}} = \left( \frac{M_{M}}{M_{E}} \right) \times \left( \frac{R_{E}}{R_{M}} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{10} \times \left( \frac{12742}{6760} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g_{M}}{g_{E}} = 0.35$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g_{M} = 9.8 \times 0.35 = 3.48{\ ms}^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.