SATHEE: Rotation 4 Question 2

Rotation 4 Question 2

3. A smooth sphere $A$ is moving on a frictionless horizontal plane with angular velocity $ω$ and centre of mass velocity $v$ . It collides elastically and head on with an identical sphere $B$ at rest. Neglect friction everywhere. After the collision their angular speeds are $ω_{A}$ and $ω_{B}$ respectively. Then,

(1999, 2M)

(a) $ω_{A} < ω_{B}$

(b) $ω_{A} = ω_{B}$

(d) $ω_{B} = ω$

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Answer:

Correct Answer: 3. (c)

Solution:

Since, it is head on elastic collision between two identical spheres, they will exchange their linear velocities, i.e., $A$ comes to rest and $B$ starts moving with linear velocity $v$ . As there is no friction anywhere, torque on both the spheres about their centre of mass is zero and their angular velocities remain unchanged. Therefore,

$ω_{A} = ω and ω_{B} = 0 .$

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Rotation 4 Question 2

3. A smooth sphere A is moving on a frictionless horizontal plane with angular velocity ω and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are ωA and ωB respectively. Then,

Answer:

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