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Question

All the surfaces shown in the figure are frictionless. The mass of the inclined wedge is M, that of the block is m and spring constant of the spring is k. Initially, the block and wedge are at rest. The spring is stretched by a small length and then released. Find the time period of oscillation of the system.


A
2πMk
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B
2πMk
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C
2πm+M2k
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D
2πMmk(m+M)
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Solution

The correct option is D 2πMmk(m+M)
Since the block and wedge will oscillate together, we can use the concept of reduced mass.
Reduced mass (μ) of system is given by
μ=mMm+M
and Time period (T)=2πμkeq
Here, keq=k & μ=mMm+M
So, T=2πmMk(m+M)

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