A cubic block of mass m is sliding down on an inclined plane at 60° with an acceleration of , the value of coefficient of kinetic friction is [2025]

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Solution

Q.
A cubic block of mass m is sliding down on an inclined plane at 60° with an acceleration of $\frac{g}{2}$ , the value of coefficient of kinetic friction is [2025]

1 $\sqrt{3} - 1$

2 $\frac{\sqrt{3}}{2}$

3 $\frac{\sqrt{2}}{3}$

4 $1 - \frac{\sqrt{3}}{2}$

Ans.
(1)

$a = \frac{m g \sin 60 ° - μ m g \cos 60 °}{m} = \frac{g \sqrt{3}}{2} - \frac{μ g}{2}$

$\Rightarrow \frac{g}{2} = \frac{g}{2} (\sqrt{3} - μ) \Rightarrow \sqrt{3} - μ = 1$

$\Rightarrow μ = (\sqrt{3} - 1)$

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