As illustrated in the figure, a small wheel is fixed coaxially onto a larger wheel of double the radius. The entire system rotates about their common axis. The strings supporting $A$ and $B$ do not slip over the wheels. If $x$ and $y$ represent the distances travelled by $A$ and $B$ during the same time interval, then

Question

As illustrated in the figure, a small wheel is fixed coaxially onto a larger wheel of double the radius. The entire system rotates about their common axis. The strings supporting

A

and

B

do not slip over the wheels. If

x

and

y

represent the distances travelled by

A

and

B

during the same time interval, then
As illustrated in the figure, a small wheel is fixed coaxially onto a larger wheel of double the radius. The entire

As illustrated in the figure, a small wheel is fixed coaxially onto a larger wheel of double the radius. The entire

Quantrex Academy · Accepted Answer

Correct answer: A. y = 2x

Let the radius of the smaller wheel be r . According to the problem, the radius of the larger wheel is R = 2r . Since both wheels are fixed coaxially, they rotate together and undergo the same angular displacement θ in a given time interval. The string supporting block A is wound around the smaller wheel. Therefore, the distance travelled by A is: x = rθ The string supporting block B is wound around the larger wheel. Therefore, the distance travelled by B is: y = Rθ = (2r)θ Substituting rθ = x into the equation for y , we get: y = 2x

As illustrated in the figure, a small wheel is fixed coaxially onto...

Options

Correct answer

Step-by-step solution

More from Rotational Mechanics