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A block is tied within two spring, each ...

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 it reaches equilibrium is `sqrt(3l_(0))` then the mass of the block is:

A

`(2kl_(0))/(g)`

B

`(sqrt(2)kl_(0))/(g)`

C

`(sqrt(3)kl_(0))/(g)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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_(0) +x_(0) =sqrt(l_(0)^(2)+3l_(0)^(2)) = 2l_(0) rArr x_(0) = l_(0)`
`mg = [kx_(0) sin 60^(@)]2 = sqrt(3) kl_(0) rArr m = (sqrt(3)kl_(0))/(g)`
`tan theta = sqrt(3) rArr theta = 60^(@)`
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Knowledge Check

  • 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:

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

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    A
    `(2gl_(0))/(sqrt(2))`
    B
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    C
    `(4gl_(0))/(sqrt(3))`
    D
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    A
    mg
    B
    mg/2
    C
    3mg/2
    D
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