Practice portal › Work, Energy and Power › Work Done by Gravity, Friction and Contact Forces

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

Asked in JEE Main 2016 · Work done by friction

• (1) 0.2 and 6.5 m
• (2) 0.2 and 3.5 m
• (3) 0.29 and 3.5 m
• (4) 0.29 and 6.5 m

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives this pair. Sanity check: x is fixed by geometry alone as 4 cos 30°=3.46 m.
• (2) Comes from a slip in μ=h/2x (e.g. using x=5 m) after getting x right.
• (4) No single slip gives 6.5 m; the equal-loss condition ties x to PQ cos 30°=3.46 m.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.