Question

A particle moves along a circle of radius r with constant tangential acceleration. If the velocity of the particle is v at the end of second revolution, after the revolution has started, then the tangential acceleration is ______.

Options

• `"v"^2/(8pi"r")`

• `"v"^2/(6pi"r")`

• `"v"^2/(4pi"r")`

• `"v"^2/(2pi"r")`

Answer 1

A particle moves along a circle of radius r with constant tangential acceleration. If the velocity of the particle is v at the end of second revolution, after the revolution has started, then the tangential acceleration is `underlinebb("v"^2/(8pi"r"))`.

Explanation:

Using third equation of motion,

v² = u² + 2as                        ...(i)

We have given

Initial velocity, u = 0

S = 2 × 2πr = 4πr

So, v² = 2a × 4πr 

⇒ a = `"V"^2/(8pi"r")`    (using (i))