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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

Question Image
Grade:12

1 Answers

Adarsh Pal
askIITians Faculty 159 Points
one year 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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