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 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:
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^(@)`
`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 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
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 block is under equilibrium and the angle made by the spring with horizontal is 60^(@) then the mass of the block is:
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 block is under equilibrium and the angle made by the spring with horizontal is 60^(@) then the mass of the block is:
A
`(2gl_(0))/(sqrt(2))`
B
`(sqrt(2)gl_(0))/(sqrt(3))`
C
`(4gl_(0))/(sqrt(3))`
D
None of these
Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.
Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.
A
mg
B
mg/2
C
3mg/2
D
2 mg