Point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30° in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be: 

Concept: 

Restoring force concept is being used in this question which can be explained as:

A force that acts to return a body to its equilibrium position is known as the restoring force. The restoring force is always directed back toward the equilibrium position of the system and depends only on the position of the mass or particle. It is the force that brings something to its original size and shape.

 F = m ω² A      ------(1) 

Calculations:

Given: 

The point ‘A’ covers 30⁰ in 0.1 sec.

Means, time period for covering area is:

For π/6, degree coverage of the area, we need time = 0.1 sec

For one degree time required is = 0.1/(π/6)

For covering complete circle degrees are = 2π

For completing the circle time period required is (T)= 0.1×6×2π/π

T = 1.2 sec      -----(2)

We know, that Angular frequency, ω = 2π/T   -----(3)

Using equations (3) and (2) we get:

ω = 2π/1.2

Using equation (1) we get:

Restoring force (F) = mω²A

Then, Restoring force per unit mass (F/m) = ω² A

F/m = (2π/1.2)² x 0.36

≃ 9.87 N

Hence, option (2) is correct.