A belt connects a pulley of 2-inch radius with a pulley of 5-inch radius. If the smaller pulley turns through 50 radians, through how many radians will the larger pulley turn?

Answer 1

The relationship between the radii and the angles turned by the pulleys is given by the formula:

radius_1 * angle_1 = radius_2 * angle_2

Plugging in the given values:

2 * 50 = 5 * angle_2

100 = 5 * angle_2

Dividing both sides of the equation by 5:

20 = angle_2

The larger pulley will turn through 20 radians. Answer: \boxed{20}.