Question

If radius of earth contracted by 0.1% its mass remaining same,then weight of the body at earth's surface will increase by

• A. 0.1%
• B. 0.2%
• C. 0.3%
• D. Remains same

Answer 1

The correct option is B 0.2%

If radius is decreased by 0.1%

$r^{\prime }=r-0.001r=0.999r$

$W^{\prime }=\frac{GMm}{(0.999r{)}^2}=\frac{GMm}{(0.999{)}^2{r}^2}$

$=\frac{W}{{0.999}^2}$

$=1.002W$

$\Delta W=W^{\prime }-W=0.002$

$0.002\times 100=0.2$% increase.