MHT CET · Physics · Motion In Two Dimensions

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in $m / s^{2}$ is

A $2 π^{2}$
B $8 π^{2}$
C $π^{2}$
D $4 π^{2}$

Verified Solution

Answer & Solution

Correct Answer

(D) $4 π^{2}$

Step-by-step Solution

Detailed explanation

Given, diameter of circle, d = 50 cm

= 50 \times 10^{- 2} m

And frequency, f = 2 Hz
The acceleration of particle in a uniform circular motion can be given as

a = ω^{2} x

Where,

ω

= angular frequency =

2 π f

X = distance from centre

= \frac{d}{2}

\Rightarrow a = 4 π^{2} f^{2} \times \frac{d}{2}

… (i)
Substituting given values in Eq. (i), we get

a = 4 π^{2} \times 4 \times \frac{50 \times 10^{- 2}}{2} = 4 π^{2}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m/s2 is

Step-by-step Solution

A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in $m / s^{2}$ is