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  • In case (i) plane is smooth and in case (ii) plane is rough. If the time taken by the block in case (ii) to come down is 3 times to the time to come down in case (i) then the coefficient of fr

In case (i) plane is smooth and in case (ii) plane is rough. If the time taken by the block in case (ii) to come down is 3 times to the time to come down in case (i) then the coefficient of friction of plane in case (ii) is?

Option: 1

\frac{1}{3}


Option: 2

\frac{2}{3}


Option: 3

\frac{3}{4}


Option: 4

\frac{1}{2}


Answers (1)

best_answer

Length covered in both cases is same so for smooth wedge s =ut + \frac{1}{2}at^2

s_1 =\frac{1}{2}at^2

s_1 =\frac{1}{2}g\sin\theta t^2\;\;\; -(I)\;\;\left[a = g\sin\theta \right ]

For rough wedge s_2 =\frac{1}{2}g(\sin\theta-\mu\cos\theta) (nt)^2\;\;\; -(II)\;\;\left[a = g(\sin\theta-\mu\cos\theta) \right ]

Now s_1 = s_2

\frac{1}{2}g\sin\theta t^2 = \frac{1}{2}g\left(\sin\theta - \mu\cos\theta\right)(nt)^2

Solving

\mu = \tan\theta\left[1-\frac{1}{n^2} \right ]

    = \frac{3}{4}\left[1-\frac{1}{3^{2}} \right ] = \frac{3}{4} \times \frac{8}{9} \Rightarrow \frac{2}{3}

Posted by

Gautam harsolia

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