A rocket is fired vertically from the earth with an acceleration of \(2g\), where \(g\) is the gravitational acceleration. On an inclined plane inside the rocket, making an angle \(\theta\) with the horizontal, a point object of mass \(m\) is kept. The minimum coefficient of friction \(\mu_{\min}\) between the mass and the inclined surface such that the mass does not move is :
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- \(\tan\theta\)
- \(2\tan\theta\)
- \(3\tan\theta\)
- \(\tan 2\theta\)
The Correct Option is A
Solution and Explanation
Normal reaction: \(N = 3mg\cos\theta\).
Component along the incline: \(3mg\sin\theta\).
No motion requires \(3mg\sin\theta \le \mu N = \mu\,3mg\cos\theta\), so \(\mu \ge \tan\theta\).
Hence \(\mu_{\min}=\tan\theta\).
Answer: (1) \(\tan\theta\)
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