Question

A particle starting from rest moves along the circumference of a circle of radius r with angular acceleration a. The magnitude of the average velocity, in the time it completes the small angular displacement θ is 

Options

• `"r"(2/(alpha  theta))^2`

• `"r"((alpha  theta)/2)^2`

• `rho((alpha  theta)/2)`

• `"r"((alpha  theta)/2)^(1/2)`

Answer 1

`"r"((alpha  theta)/2)^(1/2)`

Explanation:

The angular displacement of particle,

θ = ω₀t + `1/2 alpha "t"^2`

θ = `1/2 alpha "t"^2`   ....`((because "particle initially at rest"),(therefore omega_0 = 0))`

t = `((2theta)/alpha)^(1/2)`

The average velocity of particle,

`"v"_"avg" = "displacement"/"time"`

`= ("r" theta)/"t" = ("r"theta)/((2theta)/alpha)^(1/2)`

= `"r"((alpha  theta)/2)^(1/2)`