Question

A pendulum is made of a rigid rod of mass m and length l and a small bob of mass M is attached at one end. The rod is pivoted at the other end.What is the minimum speed of the bob at its lower end so that it completes a full circle?

Answer 1

Answer:

Explanation:

=> Here, A pendulum is made of a rigid rod of mass m and length l and a small bob of mass M is attached at one end. The rod is pivoted at the other end.

=> Suppose velocity of bob of pendulum is V at the lowest point.

=> According to law of energy conservation,

1/2MV^2 + 1/2qw^2 = mg(2L) + mgL

1/2MV^2 + 1/2*(mL^2/3)*(V^2/L^2) = gL (2M + m)

(3M + m)v^2 = gL (12M+6m)

V = √ gL (12M + 6m/3M+m)

Thus, the minimum speed of the bob at its lower end so that it completes a full circle is √ gL (12M + 6m/3M+m).