Question

If mass of earth decreases by $25\%$ and its radius increases by $50\%$, then acceleration due to gravity at its surface decreases by nearly:

• A. $89\%$
• B. $67\%$
• C. $33\%$
• D. $11\%$

Answer 1

The correct option is B $67\%$

we know that

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

The mass of the earth decrease by $25\%$ ,

remaining $75\%$ of

$M=\frac{75}{100}M$

radius of earth increase by $50\%$ ,

new radius $=150\%$ of $R=\frac{150}{100}R$

$g^{\prime }=\frac{G\left(\frac{75}{100}M\right)}{{\left(\frac{150R}{100}\right)}^2}$

$g^{\prime }=G\frac{M}{R^2}\left[\frac{75}{100}\times \frac{10000}{150\times 150}\right]$

$g^{\prime }=g\frac{5}{15}$

$g^{\prime }=0.33g$

The acceleration due to gravity decreases by

$=g-0.33g$

$=0.67g$

The acceleration due to gravity decreases by

$=0.67\times 100\%$

$=67\%$

Hence the acceleration due to gravity at its surface decreases by nearly $67\%$.