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, then its weight will:

• A. Decreases by $0.5\%$
• B. Decreases by $2\%$
• C. Increases by $0.5\%$
• D. Increase by $1\%$

Answer 1

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

Weight = Mg

But g = $\frac{GM}{r^2}$

Then g${}_h$ = $\frac{GM}{(r+h{)}^2}$

$\frac{g}{g_h}$ = $\frac{100}{99}$ = ($\frac{r+h}{r}$)${}^2$

$\frac{r+h}{r}$ = 1.005

r + h = 1.005r

g${}_d$ = g(1 - $\frac{d}{r}$)

d = 0.005r

g${}_d$ = 1 - 0.005 = 0.995

Thus the weight will be decreased by 0.5%.