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Two blocks of masses 1 kg and 3 kg are m...

Two blocks of masses `1 kg` and `3 kg` are moving with velocities `2 m//s` and `1 m//s` , respectively , as shown. If the spring constant is `75 N//m` , the maximum compression of the spring is

A

`5 cm`

B

`2 cm`

C

`3 cm`

D

`4 cm`

Text Solution

Verified by Experts

The correct Answer is:
B
Due to spring force , velocity of `1 kg` decreases and that of `3 kg` increases . At the maximum compression , both the blocks move with same velocity.
By the momentum conservation
` 1 xx 2 + 3 xx1 = (1 + 3)v rArr v = (5)/(4) m//s`
By the energy conservation
`(1)/(2) 1 (2)^(2) + (1)/(2) xx 3 (1)^(2) = (1)/(2) (1 + 3) v^(2) + (1)/(2) kx^(2)`
`(7)/(2) = 2((5)/(4))^(2) + (75)/( 2) x^(2) rArr (75)/(2) x^(2) = (7)/(2) - (25)/(8) = (3)/(8)`
`x^(2) = (1)/(100) rArr x = (1)/(10) m = 10 cm`
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Knowledge Check

  • In the arrangements as shown, blocks A and B of the masses as shown move in the direction with velocities as indicated on a smooth surface. The spring constant is 300 N/m. find the maximum compression in the spring (approx).

    A
    17 cm
    B
    22 cm
    C
    32 cm
    D
    38 cm

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    A
    `0.06m`
    B
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    D
    none of these

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    A
    `sqrt((2m)/(k))v_(0)`
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