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A block of mass m is pulled by a constant power P placed on a rough horizontal plane. The friction co-efficient between the block and surface varies with its speed v as $μ = \frac{1}{\sqrt{1 + v}}$ . The acceleration of the block when its speed is 3 m/s will be

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$\frac{P}{3 m}$

$\frac{P}{3 m} + \frac{g}{2}$

$\frac{g}{2}$

$\frac{P}{3 m} - \frac{g}{2}$

answer is A.

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Detailed Solution

$P = Fv$

$F = \frac{P}{3} a n d μ = \frac{1}{\sqrt{3 + 1}} = \frac{1}{2}$

$f = μ N = \frac{1}{2} mg$

$F - f = ma$

$∴ a = \frac{\frac{P}{3} - \frac{1}{2} mg}{m}$

$a = \frac{P}{3 m} - \frac{g}{2}$

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