Question

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

• A. increased 2%
• B. decreased 1.5%
• C. increased 1%
• D. decreased 1%

Answer 1

Answer: (A)

From law of gravitation.
$F=G\frac{M_{e}m}{R_e^2}$ ...(i)
Also from Newton's law
$F=mg$ ...(ii)
Equating Eqs. (i) and (ii), we get
$g=\frac{G{M}_e}{R_e^2}$
$\frac{g_1}{g_2}={\left(\frac{R_2}{R_1}\right)}^2$
$={\left(\frac{0.99R}{R}\right)}^2$
$\frac{g_1}{g_2}=0.98$
$g_2=\frac{g_1}{0.98}=1.02g_1$
Hence, change in acceleration due to gravity
$=g_2-g_1=1.02g_1-g_1=0.02g_1=2\%g_1$
Since, sign is positive, acceleration due to gravity will increase by $2\%$