A solid cylinder of mass M and radius R, rolling without sliding on a rough horizontal plane, is pulled at its axis with a horizontal velocity of $V_{0}$ . By means of string of length 2R attached to its axis, the cylinder is dragging a thin plate of mass $m = 2 M$ lying on the plane. If the system is released, then choose the correct option(s). $(μ = 0.4, V_{0} = 2 m / \sec, R = 0.5 m, g = 10 m / \sec^{2})$

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Average speed during the motion is 1 m/sec.

Distance covered before stopping is 0.49 m.

Time taken to stop is 0.96 sec.

Distance covered before stopping is 0.96 m.

answer is A, C, D.

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Detailed Solution

$F_{2} - F_{1} = (m + M) a, F_{1} R = \frac{1}{2} {MR}^{2} \frac{a_{s}}{R} F_{1} = \frac{1}{2} Ma F_{2} = μ (mg - Tsinα) Tcosα - F_{1} = {Ma}_{s} Solving these equation a_{s} = \frac{4 μ}{3 (1 + μtanα) + 4} = 2.08 m / \sec^{2} S = \frac{V_{0}^{2}}{2 a_{s}} = \frac{4}{2 \times 2.08} = 0.96 m t = \frac{u}{a} 0.96$