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The maximum compression of the spring after collision is - A 1 2 k m v 0 2 ​ ​ B 5 k m v 0 2 ​ ​ C 1 0 k m v 0 2 ​ ​ D None of these

 

The maximum compression of the spring after collision is -

 
A

12kmv02

B

5kmv02

C

10kmv02

D

None of these

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Grade:12

1 Answers

Adarsh Pal
askIITians Faculty 159 Points
2 years ago
Since the velocity of all the blocks is the same at maximum compression.
Apply conservation of momentum, it can be written as,
mv0​+2mv0​=4mv1​+mv0​
v1​=2v0​​
Thus, the velocity of block B just after the collision is 2v0​​.
Apply conservation of momentum, just before and at the time of compression it is given as,
mv0​+2mv0​=5m×v
v=53v0​​
Apply the conservation of energy, just after collision and at the time of maximum compression, it is given as,
21​mv0​2+21​×4mv1​2=21​×5mv2+21​kx2
21​mv0​2+21​×4m(2v0​​)2=21​×5m(53v0​​)2+21​kx2
21​kx2=2mv0​2​(1+1−2545​)
x2=5kmv0​2​
x=5kmv0​2​​
Thus, the maximum compression of the spring after the collision is 5kmv0​2​​.
 

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