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Q.

A plank of mass 3m is placed on a rough inclined plane and a man of mass m walks down the board. If the co-efficient of friction between the board and inclined plane is $μ = 0.5$ , the minimum acceleration of the man, so that the plank does not slide is ____

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a

$6 m s^{- 2}$

b

$8 m s^{- 2}$

c

$3 m s^{- 2}$

d

$4 m s^{- 2}$

answer is A.

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Detailed Solution

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For equilibrium of plank 3mg sin37 $= f + f_{1}$
Where $f_{1} = u m g \cos 37 = 0.5 (4 m g \cos 37) = 2 m g \cos 37^{°}$
$\frac{9}{5} m g - \frac{8}{5} m g = f \Rightarrow f = \frac{m g}{5} = 2 m$
For equilibrium of man mg sin37 + f = ma
6m + 2m = ma
$a = 8 m s^{- 2}$

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