Question

There are two bodies A and B of same mass. Ais placed near the equator of earth and B is placed at a height ‘h' above the pole of the earth. If both the bodies weigh equally. Find 'h’ in terms of radius ‘R’ of earth, angular speed ‘ w' of earth, and 'q’ acceleration duc to gravity close to earth.

Answer 1

There are two bodies A and B of same mass. A is placed near the equator of earth and B is placed at height h above the pole of the earth.

To find : if both the bodies weigh equally. we have to find h in terms of radius R of earth, angular speed ω of earth.

solution : have a look underlined line, here question said “ both the bodies weigh equally” it means effective g same for both bodies.

for A , $g_A=g-\omega^2R$ [ A is placed at equator ]

for B, $g_B=g\left(1-\frac{2h}{R}\right)$

now $g_A=g_B$

⇒$g-\omega^2R=g\left(1-\frac{2h}{R}\right)$

⇒$1-\frac{\omega^2R}{g}=1-\frac{2h}{R}$

⇒$h=\frac{omega^2R^2}{2g}$

Therefore the correct option is (2) ω²R²/2g