Question

Two identical simple pendulums A and B are fixed at same point. They are displaced by very small angles a and b ( b>a) and released from rest. Find the time after which B reaches its initial position for the first time. Collisions are elastic and length of strings is l.

• A. $\pi\sqrt{\frac{\mathcal{l}}{g}}$
• B. $2\pi\sqrt{\frac{\mathcal{l}}{g}}$
• C. $\frac{\pi\beta}{\alpha}\sqrt{\frac{\mathcal{l}}{g}}$
• D. $\frac{2\pi\beta}{\alpha}\sqrt{\frac{\mathcal{l}}{g}}$

Answer 1

Answer: (B)

$2\pi\sqrt{\frac{\mathcal{l}}{g}}$

Answer 2

Time period of both A and B T = 2p $\sqrt{\frac{\mathcal{l}}{g}}$

After first collision, B acquires amplitude of A and after second collision it acquires its own amplitude in this process time taken is

= $\frac{T}{4}$+ $\frac{T}{4}$+ $\frac{T}{4}$+ $\frac{T}{4}$ = T = $2\pi\sqrt{\frac{\mathcal{l}}{g}}$