Question

An object is placed on an inclined plane. The angle of incline is gradually increased until the object begins to slide. The angle at which this occurs is θ, what is the coefficient of static friction between the object and the plane?

A) cos θ
B) sin θ
C) 1/tan θ Sin
D)tan θ
E) None of these

Answer 1

D)
`\tan\theta`

Step-by-step explanation:

Let m be the mass of object .

Angle =
`\theta`

We have to find the coefficient of static friction between the object and the plane.

Normal ,N=
`mgcos\theta`

Force, F=f(Friction force)

`mgsin\theta=\mu N`

Substitute the values

`mgsin\theta=\mu mgcos\theta`

`\mu=(mgsin\theta)/(mgcos\theta)`

`\mu=tan\theta`

`tan\theta=(sin\theta)/(cos\theta)`

Where
`\mu=` Coefficient of static friction

Hence option D is true.