A block is tied within two spring, each having spring constant equal to `k`. Initially the springs are in their natural length and horizontal as shown. The block is released from rest. The springs are ideal, acceleration due to gravity is `g` downwards. Air resistance is to be neglect. The natural length of spring is `l_(0)`.

If the decrease in height of the block till its speed becomes zero is `sqrt(8l_(0))` then the mass of the block is:

Options

A. `(2kl_(0))/(g)`
B. `(sqrt(2)kl_(0))/(g)`
C. `(sqrt(3)kl_(0))/(g)`
D. None of these

Answer

B

Explanation

A block is tied within two springs, each having spring constant equal to `k`. Initially the springs are in their natural length and horizontal as shown. The block is released from rest. The springs are ideal, acceleration due to gravity is `g` downwards. air resistance is to be neglect. The natural length of spring is `l_(0)`.

`l + x = sqrt(8l_(0)^(2) +l_(0)^(2)) = 3l_(0) rArr = 2l_(0)`

`0 +0 + mg sqrt(8l_(0)) = 0+ [(1)/(2)k(2l_(0))^(2)] xx2+0`
`rArr k4l_(0)^(2) = mg sqrt(8l_(0)) rArr m = (4kl_(0))/(gsqrt(8)) = (sqrt(2)kl_(0))/(g)`