Question

If the radius of the earth is increased by three times, keeping the mass constant, then the weight of a body on the earth surface will be ______ as compared to its previous value.

• A. one third
• B. one ninth
• C. three times
• D. nine times

Answer 1

Answer: (B)

one ninth

Weight of a body is $W=mg=\frac{GMm}{R^2}$
When radius is tripled, without any change in mass of earth ($M$),
New weight would be:
$W^{\prime }=\frac{GMm}{(3R{)}^2}=\frac{1}{9}\frac{GMm}{R^2}=\frac{W}{9}$