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

Answer 1

The correct option is A

decrease by 0.5%

Percentage change in g when the body is raised to height h, $\frac{\Delta g}{g}\times 100\%=\frac{2h\times 100}{R}=1\%$
Percentage change in g when the body is taken into depth d, $\frac{\Delta g}{g}\times 100\%=\frac{d}{R}\times 100\%=\frac{h}{R}\times 100\%$ [As d =h]
$\therefore$ Percentage decrease in weight $=\frac{1}{2}(\frac{2h}{R}\times 100)=\frac{1}{2}$ (1%)=0.5%