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Question

A ball hanging from a support by an inextensible string of length l is strucked perfectly inelastically by an identical ball of mass m moving with horizontal velocity of u=2gl. Assuming the balls execute circular motion just after collision, find the tension in the string just after collision.


A
mg
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B
3mg
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C
2mg
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D
0
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Solution

The correct option is B 3mg

Given:
Collision is perfectly inelastic, therefore both ball will stick to each other and share common velocity (v) after collision.

As there are no external force in horizontal direction.
Using conservation of linear momentum of the system of bodies just before and after collision,
mu=(m+m)vv=u2 ...(i)

After the collision body starts circular motion of radius l



Tension in the string is T,
T2mg=2mac=2m(v2l) ...(ii)
Using equation (i) and (ii)
T=2mu24l+2mg
Given:
u=2gl
T=mg+2mg=3mg

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