Question

Weight of a body of mass m decreases by $1\%$ when it is raised to height $h$ above the earth's surface. If the body is taken to a depth $h$ in a mine, change in its weight is:

• A. by $0.5\%$ decrease
• B. by $2\%$ decrease
• C. by $0.5\%$ increase
• D. by $1\%$ increase

Answer 1

The correct option is A by $0.5\%$ decrease

Apparent acceleration due to gravity at height $h$, $g^{\prime }=g(1-\frac{2h}{R})$

$⟹$ $\frac{g-g^{\prime }}{g}=\frac{2h}{R}$

$\therefore$ Percentage decrease in weight, $\frac{mg-m{g}^{\prime }}{mg}\times 100=\frac{2h}{R}\times 100$

$⟹$ $\frac{2h}{R}\times 100=1$ %

OR $\frac{h}{R}\times 100=0.5$ % .............(1)

Apparent acceleration due to gravity at depth $h$, $g_1^{\prime }=g(1-\frac{h}{R})$

$⟹$ $\frac{g-g_1^{\prime }}{g}=\frac{h}{R}$

$\therefore$ Percentage decrease in weight, $\frac{mg-m{g}_1^{\prime }}{mg}\times 100=\frac{h}{R}\times 100=0.5$ % (using (1))