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On a smooth inclined plane, a body of ma...

On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant K , the period of oscillation of the body (assuming the springs as massless) is

A

`(1)/(2 pi) sqrt((k)/( 2 M))`

B

`(1)/(2 pi) sqrt((2k)/( M))`

C

`(1)/(2 pi) sqrt((2k)/( Mg sin alpha))`

D

`(1)/(2 pi) sqrt((k)/( Mg sin alpha ))`

Text Solution

Verified by Experts

The correct Answer is:
B

`K_(eq) = K_(1) + K_(2) = k + k = 2k`
`T = 2 pi sqrt(( M)/( k_(eq))) = 2 pi sqrt((M)/(2k))`
`f = (1)/(T) = (1)/(2 pi) sqrt((2 k)/( M))`
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