First slide

Rolling motion

Question

A ring is rolling without slipping on a plane surface as shown in figure. If speed of A is 4 m/s, speed of B is

Moderate

A

$2 \sqrt{2} m/s$
B

$2 m/s$
C

$\sqrt{2} m/s$
D

$4 \sqrt{2} m/s$

Solution

If $ω$ be its angular velocity and since O is the instantaneous centre of rotation, then $V_{A} =ω×OA$ and $V_{B} =ω×OB$
$∴ \frac{V_{B}}{V_{A}} = \frac{ω \times OB}{ω \times OA} = \frac{\sqrt{2} R}{2 R} \Rightarrow \frac{V_{B}}{V} = \frac{1}{\sqrt{2}} \Rightarrow V_{B} = 2 \sqrt{2} m / s$

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