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A body is of mass 1 kg falls freely from...

A body is of mass 1 kg falls freely from a height of 100 m. on a platform of mass 3 kg which is mounted on a spring having spring constant `k=1.25 xx 10 ^6 N//m`.The body sticks to the platform and the spring's maximum compression is found to be x .Given that `g=10 ms ^-2` ,the value of x will be calose to :

A

40 cm

B

80 cm

C

2cm

D

8cm

Text Solution

Verified by Experts

The correct Answer is:
C
Initial compression in negligible
Compression will be significant due to collision velocity after collision
`1 xx sqrt( 2 xx 10 xx 100) = 4 xx v rArr v = 5 sqrt(5) m // s `
Assuming this as maximum velocity, v ` = omega A `
`5 sqrt(5) = sqrt(( 1 . 25 xx 10^(6))/( 4)) A `
`A = 5 xx 2 xx 2 xx 10 ^(-3) m = 2 cm`
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