Question

A man weighs $200$ pounds on earth.
How much would he weigh on a planet four times as massive as the earth with a radius five times as great?

• A. $4000pounds$
• B. $250pounds$
• C. $160pounds$
• D. $10pounds$
• E. $32pounds$

Answer 1

Answer: (E)

$32pounds$

Let the mass and radius of earth be $M$ and $R$ respectively.

Weight of man on earth, $F=\frac{GMm}{R^2}=200$ pounds

Mass of the planet $M^{\prime }=4M$

Radius of the planet $R^{\prime }=5R$

Weight of man on planet, $F^{\prime }=\frac{G\left(4M\right)m}{(5R{)}^2}=\frac{4F}{25}$

$⟹$ $F^{\prime }=\frac{4\times 200}{25}=32$ pounds