Question

Figure (10-Q3) 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 distance travelled by A and B in the same time interval, then
(a) x = 2 y
(b) x = y
(c) y = 2 x
(d) none of these.
Figure

Answer 1

(c) y = 2 x

It is given that angular velocity is same for both the wheels.
Therefore, we have:
v_A = $\omega$R
v_B = $\omega$2R
x = v_At = $\omega$Rt ... (i)
y = v_Bt = $\omega$(2R)t ... (ii)
From equations (i) and (ii), we get:
y = 2 x