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A uniform rod of length  and mass  is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Figure. There is no friction at the pivot. An inelastic ball of mass  is fixed with the rod at a distance  from  A horizontal impulse  is given to the rod at a distance  from  in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse  acts for a small time interval t

Now answer the following question

Find the resulting instantaneous angular velocity of the rod after the impulse

a)

b)

c)

d)



Question ID - 101341 | SaraNextGen Top Answer

A uniform rod of length  and mass  is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in Figure. There is no friction at the pivot. An inelastic ball of mass  is fixed with the rod at a distance  from  A horizontal impulse  is given to the rod at a distance  from  in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse  acts for a small time interval t

Now answer the following question

Find the resulting instantaneous angular velocity of the rod after the impulse

a)

b)

c)

d)

1 Answer
127 votes
Answer Key / Explanation : (b) -

(b)

Let the system starts with angular velocity . Angular velocity of the ball will also be  as it remains struck to the rod

Velocity of the ball

For the rod, angular impulse= change in angular momentum:

     (i)

For the ball, impulse= change in linear momentum

     (ii)

From Eqs. (i) and (ii),

and

Let impulse on the pivot be

For the rod and ball system, total impulse  change in linear momentum

Solve to get:

127 votes


127