Question

Figure below shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If 'x' and 'y' be the distances travelled by A and B in the same time interval, then

• A. x = 2y
• B. x = y
• C. y = 2x
• D. None of these

Answer 1

The correct option is C y = 2x

Linear displacement (S) = Radius (r) $\times$ Angular displacement ($\theta$)
$\therefore S\propto r(if\theta =constant)$
$\frac{DistancetravelledbymassA\left(x\right)}{DistancetravelledbymassA\left(y\right)}=\frac{RadiusofpulleyconcernedwithmassA\left(r\right)}{RadiusofpulleyconcernedwithmassA\left(2r\right)}=\frac{1}{2}\Rightarrow y=2x.$