Question

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/s²)

Options

• 1.6

• 4.0

• 2.0

• 2.5

Answer 1

2.0

Explanation:

Step 1: Draw free body diagram and Resolving forces  .....[Figure]

Let f be the frictional force

As shown in the figure: Resolving force mg along the inclined plane, we get mg sin θ

Resolving force mg perpendicular to the incline, we get mg cos θ

Step 2: Net force on block

Since the block is at rest, therefore net force acting on it along inclined direction is zero.

`sumF_("net")` = 0

⇒ f − mg sin θ = 0

⇒ 10 = m × 10 × sin30°

⇒ m = 2.0 kg