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

Answer:

(b) x = y

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Answer 2

(c) y = 2 x

If x and y be the distance traveled by A and B in the same time interval then  y = 2 x for a small wheel fixed co-axially on a bigger one of double the radius when the system rotates about the common axis.

Explanation:

It is given that angular velocity is same for both the wheels.

Angular velocity :- Angular velocity, also known as rotational velocity, is a quantitative expression of the amount of rotation per unit of time a spinning object undergoes.

It is a vector quantity which consists of a component of angular velocity and either of two given directions or senses.

Therefore

we have:

$\mathrm{v}_{\mathrm{A}}=\omega \mathrm{R}$

$\mathrm{v}_{\mathrm{B}}=\omega 2 \mathrm{R}$

$x=v_{A} t=\omega R t$   … ….. equation (i)

$y=v B t=\omega(2 R) t$ ...  …. equation  (ii)

From I and (ii) equations,  

we get:

$y=v_{B} t=2 \omega R t$                     y = 2 x

For a small wheel fixed co-axially on a bigger one of double the radius, which rotates about the common axis. The strings supporting A and B do not slip on the wheels, with x and y be the distance traveled by A and B in the same time interval , then y = 2 x