A point particle of mass, moves along the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu\). The particle is released, from rest, from the point \(P\) and it comes to rest at a point \(R\). The energies, lost by the ball, over the parts, \(PQ\) and \(PR\), of the track, are equal to each other, and no energy is lost when particle changes direction from \(PQ\) to \(QR\). The values of the coefficient of friction \(\mu\) and the distance \(x(=QR)\) are, respecitvely close to

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Answer & Solution

Correct Answer

(A) \(0.29 \) and \(3.5 \) \(m\)

Detailed explanation

Energy lost over path \(\mathrm{PQ}\) is \(=\mu \mathrm{mg} \cos \theta \times 4\)

Energy lost over path \(\mathrm{QR}\) is \(=\mu \mathrm{mgx}\)

\(\mu \mathrm{mg} \mathrm{x}=\mu \mathrm{mg} \cos \theta \times 4\)

\(x=\cos \theta \times 4\)

\(\mathrm{x}=2 \sqrt{3}=3.45 \mathrm{m}\)

From \(Q\) to \(R\) energy loss is half of the total energy loss.

\(\mu \operatorname{mg} \mathrm{x}=\frac{1}{2} \times \mathrm{mgh} \Rightarrow \mu=0.29\)

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