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A thin circular ring of mass 100 kg and radius 2 m resting on a smooth surface is subjected to a sudden application of a tangential force of 300 N at a point on its periphery. The angular acceleration of the ring will be
  • a)
    1.0 rad/sec2
  • b)
    1.5 rad/sec2
  • c)
    2.0 rad/sec2
  • d)
    2.5 rad/sec2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A thin circular ring of mass 100 kg and radius 2 m resting on a smooth...

Consider a mass m rotating around an axis, a distance r away.
Newton’s second law: F = ma
We know a = αr
(a = tangential acceleration; α = angular acceleration)
F = ma = mrα
Calculation:
F = ma = m r α
300 = 100 × 2 × α
α = 1.5 rad/s2
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Most Upvoted Answer
A thin circular ring of mass 100 kg and radius 2 m resting on a smooth...
Given data:
Mass of the ring (m) = 100 kg
Radius of the ring (r) = 2 m
Tangential force applied (F) = 300 N

We need to find the angular acceleration (α) of the ring.

The torque (τ) acting on the ring can be calculated using the equation:

τ = rF

where r is the radius of the ring and F is the tangential force applied.

Substituting the given values, we get:

τ = (2 m)(300 N)
τ = 600 Nm

The torque is also related to the angular acceleration (α) and the moment of inertia (I) of the ring through the equation:

τ = Iα

The moment of inertia (I) of a thin circular ring is given by:

I = mr²

where m is the mass of the ring and r is the radius of the ring.

Substituting the given values, we get:

I = (100 kg)(2 m)²
I = 400 kgm²

Now, we can equate the two expressions for torque:

τ = Iα

600 Nm = 400 kgm² × α

Dividing both sides by 400 kgm², we get:

α = 600 Nm / 400 kgm²
α = 1.5 rad/sec²

Therefore, the angular acceleration of the ring is 1.5 rad/sec².

Hence, the correct answer is option B.
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A thin circular ring of mass 100 kg and radius 2 m resting on a smooth surface is subjected to a sudden application of a tangential force of 300 N at a point on its periphery. The angular acceleration of the ring will bea)1.0 rad/sec2b)1.5 rad/sec2c)2.0 rad/sec2d)2.5 rad/sec2Correct answer is option 'B'. Can you explain this answer?
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