A point particle of mass $m,$ moves long 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 point $R.$ The energies, lost by the ball, over the parts, $PQ$ and $QR$, of the track, are equal to each other , and no energy is lost when particle changes direction from $PQ$ to $QR$. The value of the coefficient of friction $\mu $ and the distance $x$ $(=QR),$ are, respectively close to:

Question

A point particle of mass $m,$ moves long 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 point $R.$ The energies, lost by the ball, over the parts, $PQ$ and $QR$, of the track, are equal to each other , and no energy is lost when particle changes direction from $PQ$ to $QR$.

The value of the coefficient of friction $\mu $ and the distance $x$ $(=QR),$ are, respectively close to:

$0.29$ and $3.5$ $m$

$0.29$ and $6.5$ $m$

$0.2$ and $6.5$ $m$

$0.2$ and $3.5$ $m$

Solution

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