question_answer

The weight of a body decreases by\[x%\]when its is taken to a height of 0.5 km above the surface of the earth. If the same body is taken to a depth of 0.5 km from the surface of the earth, its weight would decrease by (a) \[2x%\]                          (b) \[x%\] (c) \[x/2%\]                        (d) \[{{x}^{2}}%\]

Answer:

Say the weight of the body decreases by y% when taken to a depth 0.5km. \[\frac{{{\omega }_{h}}}{{{\omega }_{d}}}=\frac{{{g}_{h}}}{{{g}_{d}}}\Rightarrow \frac{\frac{100-x}{100}}{\frac{100-y}{1\,\omega }}=\frac{g\left( 1-\frac{2h}{R} \right)}{g\left( 1-\frac{d}{R} \right)}\]