How much deep inside earth ( radius r ) should a man go , so that his weight becomes 1/4 of that one the earth surface?
↵If the weight has to be 1/4 of the original, then new weight = mg/4,
therefore, the new gravitational force = g/4 (mg/4÷m) Now,
g/4 = g(1-h/Re) ⇒1-h/Re=1/4 ⇒Re-h/Re=1/4 ⇒4(Re-h)=Re ⇒4Re-4h=Re ⇒4h=4Re-1Re ⇒4h=3Re ⇒h=3Re/4
therefore, the new gravitational force = g/4 (mg/4÷m) Now,
g/4 = g(1-h/Re) ⇒1-h/Re=1/4 ⇒Re-h/Re=1/4 ⇒4(Re-h)=Re ⇒4Re-4h=Re ⇒4h=4Re-1Re ⇒4h=3Re ⇒h=3Re/4