A block rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block ((in kg) is .......... (Take g = 10 `m//s^(2)`)

Options

A. 2.0 kg
B. 4.0 kg
C. 1.6 kg
D. 2.5 kg

Answer

A

Explanation

Weight of a block
`F= mg`

The block is at rest . Here we have taken frictional force = Downward component of weight along inclined plane
That is `f= mg sin theta :. , m= (f )/( g sin theta )`
Substituting `f= 10 N g =10 :. , m = (10)/( 10 sin 30^(@))`
But `sin theta = sin 30^(@) = (1)/(2) ` we get m = 2kg