A large number of pendulums with identical bobs (mass m) but varying lengths are suspended from a thick thread. Another pendulum of a heavier bob (mass M) is also suspended from the same thred as shown.

This pendulum with the heavier bob is used as a 'driver' to drive the other pendulums called as 'driven' pendulums. Assume that the amplitude of the driver is maintained constant (by some suitable mechanism). Let the frequency of the driver be `f_(0)`
The above pendulum is set into oscillation with an initial amplitude of 10.0 cm. Soon this pendulum comes to rest momentarily and the driver is seen to oscillate with an amplitude of 8.16 cm. Then mass M equals

Options

A. 1.5 m
B. 2 m
C. 2.5 m
D. 3 m

Answer

A

Explanation

By energy conservation
`(1)/(2) mv_(1)^(2)=(1)/(2)Mv_(2)^(2)`
`(1)/(2) m omega^(2) A_(1)^(2)=(1)/(2) M omega^(2) A_(2)^(2)`
`(m xx 10^(2))/((8.16)^(2)) = M = 1.5 m`
Now only one of the driven pendulums us oscillated. The driver and all other driven pendulums are clamped.