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Physics-

General

Easy

Question

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 support. If each spring has force constant k, the period of oscillation of the body (assuming the springs as massless) is

$2 π [M / 2 k]$ ^1/2
$2 π [2 M / k]$ ^1/2
$2 π [M g \sin θ / 2 k]$ ^1/2
$2 π [2 M g / k]$ ^1/2

The correct answer is: $2 pi left square bracket M divided by 2 k right square bracket$ ^1/2

It is a system of two springs in parallel. The restoring force on the body is due to springs and not due to gravity pull. Therefore slope is irrelevant. Here the effective spring constant $equals k plus k equals 2 k$
Thus time period, $T equals 2 pi square root of M divided by 2 k end root$

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