In the device shown in the figure, the block of mass 20 kg is displaced down slighty and released, it starts oscillating. Pulleys are smooth and massless, strings and springs are also massless. Find the time period of oscillation `(K_(1) = 4 N//m, K_(2) = 4N//m)`

Options

A. `2 pi s`
B. `4 pi s`
C. `10 pi s`
D. `pi s`

Answer

C

Explanation

Let elongations in springs `k_(1) and k_(2) "be" x_(1) and x_(2)`. Then `2 k_(1)x_(1) = k_(2)x_(2) rArr 2x_(1) = x_(2)`
`(k_(1) = k_(2) = 4)`
Displacement of the block `x = x_(1) + 2x_(2) = 5x_(1)`
`k_(1)x_(1) = m omega^(2) x rArr omega = (k_(1)x_(1))/(m(5x_(1))) = (k_(1))/(5m) = (4)/(5(20))`
`rArr omega = (1)/(5) rArr T = (2pi)/(omega) = 10 pi`