Assertion :A spring block system is kept over a smooth surface as shown in figure. If a constant horizontal force F is applied on the block it will start oscillating simple harmonically. Reason: Time period of oscillation is less than $2 π \sqrt{\frac{m}{k}}$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
The spring elongates by $x_{o}$ unit from its natural length (point O') due to the applied force on the block so that the block is in equilibrium about axis O.
$∴ F = k x_{o} ⟹ x_{o} = \frac{F}{k}$ means that the mean position of the oscillation is changed.
When the block is displaced by small unit say $x$ , then it oscillates about O.
Net change in force experienced by the block $F^{'} = F - k (x + x_{o})$
$⟹ F^{'} = - k x$
$∴ m a = - k x ⟹ a = - \frac{k}{m} x$ which represents $S H M$
Comparing with $a = - w^{2} x$ we get $w^{2} = \frac{k}{m}$
Time period of oscillation $T = \frac{2 π}{w} = 2 π \sqrt{\frac{m}{k}}$
Hence the Assertion is correct but the Reason is incorrect.

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Assertion :A spring block system is kept over a smooth surface as shown in figure. If a constant horizontal force F is applied on the block it will start oscillating simple harmonically. Reason: Time period of oscillation is less than 2π√mk.

Assertion :A spring block system is kept over a smooth surface as shown in figure. If a constant horizontal force F is applied on the block it will start oscillating simple harmonically. Reason: Time period of oscillation is less than $2 π \sqrt{\frac{m}{k}}$ .