JEE Main 2026 · 8 Apr · Shift 2 · Physics Q32

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A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the cylinder has a translational velocity $v_o=49$ m/s, perpendicular to its axis and a rotational velocity $v_o/4R$ about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction $\mu_K=0.25$ and $g=9.8$ m/s²)

7.5

Answer and worked solution

Official answer: B

Slipping. The contact point moves forward ( $v_0>\omega_0R=v_0/4$ ), so kinetic friction $\mu Mg$ acts backward.

Speeds.

$v=49-2.45t$ .
$\omega R=12.25+\dfrac{\mu MgR^2}{I}t=12.25+2\mu g\,t=12.25+4.9t$ .

Rolling begins when they are equal: $36.75=7.35t$ , so $t=5$ s.

(B)

Topics:Rolling motion Friction

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JEE Main 2026 · 8 Apr · Shift 2, Physics question 32