Question

The 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 ______.

Options

• x = 2y

• x = y 

• y = 2x

• None of these

Answer 1

The 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 y = 2x.

Explanation:

v = ωr, since ω is the same for both wheels.

when the radius is r, v₁ = ωr

when radius is 2r, v₂ = ω(2r)

`"v"_1/"v"_2 = (omega"r")/(omega(2"r"))= 1/2`

(Here x and y are displacements of particles A & B in the same time interval.)

`((x/t))/(y/t)= 1/2`

2x = y