Question

If radius of earth contracted by 0.1% its mass remaining same then weight of the body at earth's surface will be increased by. ​

Answer 1

Answer:

If radius of earth contracted by 0.1% its mass remaining same then weight of the body at earth's surface will be increased by 0.2%

Explanation:

The radius of Earth is contracted by 0.1%,

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

Weight, W = $\frac{GMm}{r^2}$

              $\begin{array}{l}\mathrm{W}^{\prime}=\frac{\mathrm{GMm}}{(0.999 \mathrm{r})^{2}}=\frac{\mathrm{GMm}}{(0.999)^{2} \mathrm{r}^{2}} \\=\frac{\mathrm{W}}{0.999^{2}} \\=1.002 \mathrm{~W}\end{array}$

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

Percentage increase in weight is 0.002 $\times$ 100 = 0.2%