Question

A ball of mass 1.5 kg moves with constant velocity in a horizontal circular path is attached to a string of length 24 cm. If θ = 30, calculate the radius of the circular path.

a) 0.12 m
b) 0.24 m
c) 0.36 m
d) 0.48 m

Answer 1

Using trigonometric relationships, the radius of the circular path is calculated by multiplying the length of the string by the sine of the given angle, which results in a radius of 0.12 m.

Step-by-step explanation:

The student is asking about the radius of the circular path of a ball moving with constant velocity in a horizontal circle while attached to a string. Given the length of the string and the angle θ, we can use trigonometric relationships to find the radius of the circle.

The string makes an angle of 30° with the vertical, so we can use the sine function to find the radius (r) because the length of the string (l) is the hypotenuse of the right triangle formed by the string, the vertical line from the center of the circle to the ball, and the radius.
Using the sine function:
sin(θ) = θ/opposite = r/l

L = 24 cm = 0.24 m (converting cm to m)

sin(30°) = r/0.24 m

r = 0.24 m × sin(30°)

r = 0.24 m × 0.5

r = 0.12 m

Therefore, the radius of the circular path is 0.12 m, which corresponds to option (a).