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A horizontal force applied on a body on a rough horizontal surface produces an acceleration ‘a’. If coefficient of friction between the body & surface which is $μ$ is reduced to $μ /3$ , the acceleration increases by 2 units. The value of $μ$ is

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2/3 g

3/2g

3/g

1/g

answer is C.

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Detailed Solution

F = - μ N = ma \to (1)

$F = μ N + ma$

$F - \frac{μ}{3} N = m (a + 2) \to (2)$

From 1 & 2

$μ N + ma - \frac{μ}{3} N = ma + 2 m$

$\frac{2 μ N}{3} = 2 m$

$2 μ \frac{mg}{3} = 2 m$

$μ = \frac{3}{g}$

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