Question

A particle of mass m is performing UCM along a circle of radius r. The relation between centripetal acceleration a and kinetic energy E is given by

Options

• a = `"2E"/"mr"`

• a = 2Em

• a = `"E"/"mr"`

• a = `("2E"/"mr")^2`

Answer 1

a = `"2E"/"mr"`

Explanation:

Let the velocity of the particle be v.
The kinetic energy possessed by the particle in uniform circular motion,

E = `1/2 "mv"^2`

`"v"^2 = "2E"/"m"`

The acceleration of the particle in circular motion,

a = `"v"^2/"r" = (2"E"//"m")/"r" => "a" = "2E"/"mr"`