Question

A simple pendulum consisting of a mass M attached in a string of length L is released from rest at an angle a. A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle q which string makes with the vertical after hitting the pin is –

Fig.

• A. cos^–1$\left\lbrack \frac{L\cos\alpha + l}{L + l} \right\rbrack$
• B. cos^–1$\left\lbrack \frac{L\cos\alpha + l}{L - l} \right\rbrack$
• C. cos^–1$\left\lbrack \frac{L\cos\alpha - l}{L - l} \right\rbrack$
• D. cos^–1$\left\lbrack \frac{L\cos\alpha - l}{L + l} \right\rbrack$

Answer 1

Answer: (C)

cos^–1$\left\lbrack \frac{L\cos\alpha - l}{L - l} \right\rbrack$

Answer 2

At the bottom most point, square of speed of bob,

v² = 2 gL(1 – cos a)

It will rise further to a height,

h =$\frac{v^{2}}{2g}$= L(1 – cos a)

or (L – l) (1 – cos q) = L(1 – cos a)

\ q = cos^–1$\left\lbrack \frac{L\cos\alpha - l}{L - l} \right\rbrack$