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JEE Main 2019 (10 Jan, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2019 (10 Jan, Shift 1)

Q72JEE Main 2019 · 10 JAN · SHIFT 1Medium

Rolling Motion

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -

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Answer: (b)

Force $F$ at the axle, friction $f$ backward: $F - f = Ma$ , $fR = \frac{1}{2}MR^2\alpha$ with $a = R\alpha$ .
$f = \frac{1}{2}Ma \Rightarrow F = \frac{3}{2}Ma \Rightarrow a = \dfrac{2F}{3M}$ .
$\alpha = \dfrac{a}{R} = \dfrac{2F}{3MR}$ .
So the answer is (b) (options write $m$ for $M$ ).

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