Question

Object 1 is undergoing uniform circular motion at a radius of 10 cm. Object 2 is undergoing uniform circular motion at a radius of 0.2 m. If the objects have the same mass and are traveling with the same speed, which object is experiencing the larger centripetal force and why

Answer 1

Answer:

The first object is experiencing a larger centripetal force because its radius is smaller compared to the second object.

Explanation:

Given;

radius of the first object, r₁ = 10 cm = 0.1 m

radius of the second object, r₂ = 0.2 m

let the mass of the two objects, = m

let the speed of the two objects = v

The centripetal force of the first object is given by;

$F_c_1 = \frac{mv^2}{r_1} \\\\F_c_1 = \frac{mv^2}{0.1}\\\\F_c_1 = 10mv^2$

The centripetal force of the second object is given by;

$F_c_2 = \frac{mv^2}{r_2} \\\\F_c_2 = \frac{mv^2}{0.2}\\\\F_c_1 = 5mv^2$

Therefore, the first object is experiencing a larger centripetal force because its radius is smaller compared to the second object.