Question

If density of earth increases 4 times and its radius becomes half of what it is, our weight will:

• A. be 4 times its present value
• B. be doubled
• C. remain same
• D. be halved

Answer 1

The correct option is B be doubled

Weight, $w=mg=m\frac{4}{3}\pi GR\rho$
Now that: $R^{\prime }=R/2$ and ${\rho }^{\prime }=4\rho$
$\therefore \frac{w^{\prime }}{w}=\frac{R^{\prime }{\rho }^{\prime }}{R\rho }=\left(\frac{1}{2}\right)\times 4=2$
$w^{\prime }=2w$
Hence our weight will be doubled.