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

Step-by-step solution

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 in a given time interval. The string supporting block A is wound around the smaller wheel. Therefore, the distance travelled by A is: x = r The string supporting block B is wound around the larger wheel. Therefore, the distance travelled by B is: y = R = (2r) Substituting r = x into the equation for y , w