The 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

Question

The 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 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/bed7bac54828727112f38af96e2ad1d3-.png" /> (A) 100 N (B) 0.49 N (C) 50 N (D) 9.87 N

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/24b30942a5f5e05aed8be156f4b6b664-.png" /> 30° arrow 0.1 s 360° arrow 1.2 s = T ω=(2 π/ T )=(5 π/3) At M , F = m ω2 A ⇒ ( F / m )=ω2 A

Q. The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and covers 30∘ in 0.1s. 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

100 N

0.49 N

50 N

9.87 N

30∘→0.1s 360∘→1.2s=T ω=T2π​=35π​ At M,F=mω2A ⇒mF​=ω2A

$3 0^{\circ} \to 0.1 s$
$36 0^{\circ} \to 1.2 s = T$
$ω = \frac{2 π}{T} = \frac{5 π}{3}$
At $M, F = m ω^{2} A$
$\Rightarrow \frac{F}{m} = ω^{2} A$