Question

Figure 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

Answer: (C)

$y = 2x$

Answer 2

Linear displacement (S) = Radius (r) × Angular

displacement (θ)

$\therefore S \propto r$ (if $\theta =$ constant)

$\frac { \text { Distance travelled by mass } A ( x ) } { \text { Distance travelled by mass } B ( y ) } =$ $\frac{\text{Radius of pulley concerned with mass }A(r)}{\text{Radius of pulley concerned with mass }B(2r)}$ $= \frac{1}{2}$

⇒ $y = 2x$.