question_answer

A smooth block is released at rest on a\[45{}^\circ \]incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is               [AIEEE 2005]

A) \[{{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}\]

B) \[{{\mu }_{k}}=\sqrt{1-\frac{1}{{{n}^{2}}}}\]

C) \[{{\mu }_{s}}=1-\frac{1}{{{n}^{2}}}\]

D) \[{{\mu }_{s}}=\sqrt{1-\frac{1}{{{n}^{2}}}}\]

Correct Answer: A

Solution :

[a] The situation is shown in figure when friction is absent,

.(i)

When friction is present

...(ii)

Whens

From Eqs. (i) and (ii), we get

or

(given in question)

or

or

or

or         or