Question

A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in tensions at the highest and the lowest points.

OR

Show that for a body performing V.C.M., difference in tension at the lowest and highest point on vertical circle is 6mg.

Answer 1

i. Suppose a body of mass ‘m’ performs V.C.M on a circle of radius r as shown in the figure.

ii. Let, T_L = tension at the lowest point

T_H = tension at the highest point

v_L = velocity at the lowest point

v_H = velocity at the highest point

iii. At lowest point L,

iv. By law of conservation of energy,

(P.E + K.E) at L = (P.E + K.E) at H