Question

Figure shows a small wheel fixed coaxially on a bigger one of the 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 distance 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 $y=2x$

$a=r\alpha$ (no slipping)

Thus, $a_A=R\alpha$ and $a_B=2R\alpha$

$⟹a_B=2a_A$

Now, $x=0+\frac{1}{2}{a}_A{t}^2$ and $y=0+\frac{1}{2}{a}_B{t}^2$

$\frac{y}{x}=\frac{a_B}{a_A}=2$

Thus, $y=2x$