MHT CET · Physics · Rotational Motion

A disc has mass $M$ and radius $R$ . How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $ω$ in time $t$ ?

A $\frac{M R ω}{4 t}$
B $\frac{M R ω}{2 t}$
C $\frac{M R ω}{t}$
D $M R ω t$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{M R ω}{2 t}$

Step-by-step Solution

Detailed explanation

τ = I α

F \times R = \frac{M R^{2}}{2} \times \frac{ω}{t}

F = \frac{M R}{2} \times \frac{ω}{t}

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 disc has mass M and radius R. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity ω in time t?

Step-by-step Solution

A disc has mass $M$ and radius $R$ . How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $ω$ in time $t$ ?