MHT CET · Physics · Laws of Motion
A body takes \(\mathrm{n}\) times as much time to slide down a \(45^{\circ}\) rough incline as it takes to slide down a smooth \(45^{\circ}\) incline. The coefficient of friction between the body and the incline will be
- A \(\frac{1}{1-n^{2}}\)
- B \(1-\frac{1}{n^{2}}\)
- C \(\sqrt{\frac{1}{1-n^{2}}}\)
- D \(\sqrt{1-\frac{1}{n^{2}}}\)
Answer & Solution
Correct Answer
(B) \(1-\frac{1}{n^{2}}\)
Step-by-step Solution
Detailed explanation
The coefficient of friction,
Here,
\(\begin{aligned}\mu &=\tan \theta\left(1-\frac{1}{n^{2}}\right) \\\theta &=45^{\circ}\end{aligned}\)
\(\therefore\) \(\mu=\tan 45^{\circ}\left(1-\frac{1}{n^{2}}\right)=1-\frac{1}{n^{2}}\)
Here,
\(\begin{aligned}\mu &=\tan \theta\left(1-\frac{1}{n^{2}}\right) \\\theta &=45^{\circ}\end{aligned}\)
\(\therefore\) \(\mu=\tan 45^{\circ}\left(1-\frac{1}{n^{2}}\right)=1-\frac{1}{n^{2}}\)
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