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Q.

A block of weight 100N is pushed by a force F on a horizontal rough plane moves with an acceleration $1 m / \sec^{2}$ , When force is doubled its acceleration become $10 m / \sec^{2}$ . The coefficient of friction is ……………….. $(g = 10 m s^{- 2})$

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a

$0.2 m$

b

$0.4$

c

$0.6$

d

$0.8$

answer is D.

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Detailed Solution

$\begin{array}{l} m \times 1 = F - μ_{k} mg \dots \dots . . (1) \\ m \times 10 = 2 F - μ_{k} mg \dots \dots (2) \\ Equation (1) \times (2) \\ \Rightarrow 2 m = 2 F - 2 μ_{k} mg \\ \frac{10 m = 2 F + μ_{k} mg}{- 8 m = - μ_{k} mg} \\ μ_{k} = \frac{8}{g} = \frac{8}{10} = 0.8 \end{array}$

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