MHT CET · Physics · Rotational Motion

A Wheel of moment of inertia $2 k g m^{2}$ is rotating about an axis passing through centre and perpendicular to its plane at a speed $60 rad s^{- 1}$ . Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is

A $24 k g m^{2} / s$
B $48 k g m^{2} / s$
C $72 k g m^{2} / s$
D $96 k g m^{2} / s$

Verified Solution

Answer & Solution

Correct Answer

(C) $72 k g m^{2} / s$

Step-by-step Solution

Detailed explanation

I = 2 k g m^{2}, ω_{o} = 60 rad s^{- 1}

t = 5 \min = 5 \times 60 = 300 s

\propto = \frac{0 - 60}{300} = \frac{- 60}{300} = \frac{- 1}{5} rad s^{- 2}

for 2min (from starting) (2 min = 120 sec)

ω = ω_{0} + \propto t

= 60 - \frac{1}{5} \times 120 = 60 - 24

ω = 36 rad s^{- 1} a n d L = I ω = 2 \times 36 = 72 k g m^{2} s^{- 1}

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 Wheel of moment of inertia 2 kg m2 is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad s-1. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is

Step-by-step Solution

A Wheel of moment of inertia $2 k g m^{2}$ is rotating about an axis passing through centre and perpendicular to its plane at a speed $60 rad s^{- 1}$ . Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is