Question

When the radius of earth is reduced by $1$% without changing the mass, then the acceleration due to gravity will:

• A. increase by $2$%
• B. decrease by $1.5$%
• C. increase by $1$%
• D. decrease by $1$%

Answer 1

Answer: (A)

increase by $2$%

Acceleration due to gravity is given by :

$g=\frac{GM}{R^2}$

so on differentiating,

$\frac{\Delta g}{g}=-2\frac{\Delta R}{R}$ [G,M are constant]

so, when $\frac{\Delta R}{R}=(-)1\%$ (Radius decreases) then :

$\frac{\Delta g}{g}=(-2)(-1\%)=2\%$

$\therefore g$ increases by $2\%$.