Question

A disc rolls down a smooth inclined plane without slipping. An inclined plane makes an angle of 60° with the vertical. The linear acceleration of the disc along the inclined plane is ______.

(g = acceleration due to gravity, sin 30° =cos 60° `=1/2,` sin 60° = cos 30° `=sqrt3/2`)

Options

• `g/9`

• `g/6`

• `g/3`

• `g/18`

Answer 1

A disc rolls down a smooth inclined plane without slipping. An inclined plane makes an angle of 60° with the vertical. The linear acceleration of the disc along the inclined plane is `underline(g/3)`.

Explanation:

The acceleration of rolling disc is given by

`a=(gsintheta)/(1+("k"^2/"R"^2))`    where θ is the angle made by the inclined plane with the horizontal.

∴ θ = 30°, for a disc `"k"^2/"R"^2=1/2`

`therefore a=(g  sin30^circ)/(1+1/2)=g/(2xx3/2)=g/3`