Grade 12Wave Motion
The maximum compression of the spring after collision is - A12kmv02B5kmv02C10kmv02DNone of these
The maximum compression of the spring after collision is -
A
12kmv02
B
5kmv02
C
10kmv02
D
None of these
1 Answer
Adarsh Pal
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,
21mv02+21×4mv12=21×5mv2+21kx2
21mv02+21×4m(2v0)2=21×5m(53v0)2+21kx2
21kx2=2mv02(1+1−2545)
x2=5kmv02
x=5kmv02
Thus, the maximum compression of the spring after the collision is 5kmv02.
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