JEE Main 2016 · 3 Apr · Shift 1 · Physics Q3

← JEE Main 2016 · 3 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 3 of 90

A point particle of mass $m$ , moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals μ. 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 QR, 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 μ and the distance $x$ (=QR), are, respectively close to :

Track PQR: an incline from P, at height h = 2 m, down at 30° to Q on the horizontal surface, then along the horizontal to R.

0.2 and 6.5 m

0.2 and 3.5 m

0.29 and 3.5 m

0.29 and 6.5 m

Answer and worked solution

Official answer: C

PQ $=\frac h{\sin30^\circ}=4$ m. Friction losses: on PQ, $\mu mg\cos30^\circ\times4=2\sqrt3\mu mg$ ; on QR, $\mu mgx$ . Equal losses give $x=2\sqrt3\approx3.5$ m.

All of $mgh=2mg$ is lost, half on each part: $2\sqrt3\mu mg=mg$ , so $\mu=\frac1{2\sqrt3}\approx0.29$ .

Topics:Friction Work-energy theorem

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JEE Main 2016 · 3 Apr · Shift 1, Physics question 3