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A cylinder having radius $0.4 m$ , initially rotating (at t=0 ) with $ω_{0} = 54 rad / s$ is placed on a rough inclined plane with $θ = 37 °$ having friction coefficient $μ = 0.5$ . The time taken by the cylinder to start pure rolling is $(g = 10 m / s^{2})$

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(2) $2.4 s$

(1) $5.4 s$

(3) $1.4 s$

(4) 1.2 s

answer is D.

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Detailed Solution

$a = (μgcosθ) + (gsinθ) = 0.5 \times 10 \times 0.8 + 10 \times 0.6 = 10 m / s^{2} α = \frac{(μmgcosθ) R}{\frac{1}{2} {mR}^{2}} = \frac{2 μgcosθ}{R} = \frac{2 \times 0.5 \times 10 \times 0.8}{0.4} = 20 rad / s^{2}$

Pure rolling will start when,

$v = Rω or at = R (ω_{0} - αt) 10 t = 0.4 (54 - 20 t)$

Solving this equation, we get

$t = 1.2 s$

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