Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius ( r 3 ) and lighter one in a radius r . The tangential speed of lighter stone is ' n ' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of n is

Step-by-step solution

The centripetal forces are equal: F_L = F_H . For stones with masses m_L = m , m_H = 3m and radii r_L = r , r_H = r 3 , with tangential speeds related by v_L = n v_H , the force equality becomes: m (n v_H)^2 r = 3m v_H^2 r/3 Simplifying both sides yields: m n^2 v_H^2 r = 9m v_H^2 r Canceling common factors ( m , v_H^2 , and r ) from both sides gives n^2 = 9 , so n = 3 . Answer: 3