Question

If the earth shrinks half in radius with its mass remaining the same, the weight of an object on earth will :

• A. decrease by $50$%
• B. increase by $50$%
• C. decrease by $25$%
• D. increase by $300$%

Answer 1

Answer: (D)

increase by $300$%

As the mass of the earth remains same, so initially the gravitational acceleration,

$g=\frac{GM}{R^2}$ and after shrinks $g^{\prime }=\frac{GM}{(R/2{)}^2}=4g$

% change in weight $=\frac{m{g}^{\prime }-mg}{mg}\times 100=\frac{g^{\prime }-g}{g}\times =\frac{4g-g}{g}\times 100=300$ %