Question

The ratio of the weights of an object of mass $m$ at a height $R$ and $2R$ from the surface of earth is ($R$ is the radius of earth)

• A. $4:9$
• B. $1:1$
• C. $9:4$
• D. $1:2$
• E. $4:1$

Hint:

Weight varies inversely with square of distance from earth’s center: - Always use $(R + h)$ in formula, not just $h$

Answer 1

The Correct Option is C

Concept: Weight at height $h$ from earth’s surface: \[ W = \frac{GMm}{(R+h)^2} \]

Step 1: Find weight at height $R$.
\[ W_1 = \frac{GMm}{(R+R)^2} = \frac{GMm}{(2R)^2} = \frac{GMm}{4R^2} \]

Step 2: Find weight at height $2R$.
\[ W_2 = \frac{GMm}{(R+2R)^2} = \frac{GMm}{(3R)^2} = \frac{GMm}{9R^2} \]

Step 3: Find ratio.
\[ \frac{W_1}{W_2} = \frac{\frac{1}{4R^2}}{\frac{1}{9R^2}} = \frac{9}{4} \]