Question

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m/s² is ______.

Options

• 2 π²

• 8 π²

• π²

• 4 π²

Answer 1

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m/s² is 4 π².

Explanation:

Given, diameter of circle, d = 50cm

= 50 × 10^-2 m

and frequency, f = 2 Hz

The acceleration of particle in a uniform circular motion can be given as

a = ω² x

where, ω = angular frequency = 2πf

x = distance from centre = `"d"/2`

`=> "a" = 4pi^2"f"^2 xx "d"/2`    ....(i)

Substituting given values in Eq. (i), we get

a = `4pi^2 xx 4 xx (50 xx 10^-2)/2 = 4pi^2`