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

Answer: (B)

be doubled

Answer 2

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