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a hoop of radius 2 m weighs 100 kg it rolls along...

Question:
A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

Answer:

Radius of the hoop, r = 2 m

Mass of the hoop, m = 100 kg

Velocity of the hoop, v = 20 cm/s = 0.2 m/s

Total energy of the hoop = Translational KE + Rotational KE

E_r = 1/2 mv² + 1/2 I ω²

Moment of inertia of the hoop about its centre, I = mr²

E_r = 1/2 mv² + 1/2 (mr²) ω²

But we have the relation, v = rω

∴ Er = 1/2 mv² + 1/2 mr² ω²

∴ Er = 1/2 mv² + 1/2 mv²

∴ Er = mv²

The work required to be done for stopping the hoop is equal to the total energy of the hoop.

∴Required work to be done, W = mv² = 100 × (0.2)² = 4 J

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Question:
A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

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Question: A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

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Question:
A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?