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Three spheres, each of mass m, can slide...

Three spheres, each of mass `m`, can slide freely on a frictionless, horizontal surface. Spheres `A` and `B` are attached to an inextensible, inelastic cord of length `l` and are at rest in the position shown where sphere `B` is struck by sphere `C` which is moving to the right with a velocity `v_(0)`. Knowing that the cord is taut where sphere `B` is struck by sphere `C` and assuming 'head on' inelastic impact between `B` and `C`, we cannot conserve kinetic energy of the entire system.
Velocity of `A` immediately after collision is along unit vector

A

`hatj`

B

`1/2hati+sqrt(3)/2hatj`

C

`hatj`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
velocity of `A:vecv_(1)=v_(1)costhetahati+v_(1)sinthetahatj`
`impliesvecv_(1)=costhetahati+sinthetahatj=1/2hati+(sqrt(3))/2hatj`
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Three spheres, each of mass m , can slide freely on a frictionless, horizontal surface. Spheres A and B are attached to an inextensible, inelastic cord of length "l" and are at rest in the position shown where sphere B is struck by sphere C which is moving to the right with a velocity v_(0) . Knowing that the cord is taut where sphere B is struck by sphere C and assuming "Head on" inelastic impact between B and C , we can 't conserve kinetic energy of entire system. The velocity of B immediately after collision is along unit vector

Three spheres, each of mass m , can slide freely on a frictionless, horizontal surface. Spheres A and B are attached to an inextensible, inelastic cord of length "l" and are at rest in the position shown where sphere B is struck by sphere C which is moving to the right with a velocity v_(0) . Knowing that the cord is taut where sphere B is struck by sphere C and assuming "Head on" inelastic impact between B and C , we can 't conserve kinetic energy of entire system. Velocity of A immediately after collision is along unit vector

Knowledge Check

  • Three spheres, each of mass m , can slide freely on a frictionless, horizontal surface. Spheres A and B are attached to an inextensible, inelastic cord of length l and are at rest in the position shown where sphere B is struck by sphere C which is moving to the right with a velocity v_(0) . Knowing that the cord is taut where sphere B is struck by sphere C and assuming 'head on' inelastic impact between B and C , we cannot conserve kinetic energy of the entire system. The magnitude of velocity of A immediately after collision is

    A
    `sqrt(3v_(0))/4`
    B
    `(v_(0))/8`
    C
    `(v_(0))/4`
    D
    `(sqrt(mv_(0)))/8`

  • Three spheres, each of mass m , can slide freely on a frictionless, horizontal surface. Spheres A and B are attached to an inextensible, inelastic cord of length l and are at rest in the position shown where sphere B is struck by sphere C which is moving to the right with a velocity v_(0) . Knowing that the cord is taut where sphere B is struck by sphere C and assuming 'head on' inelastic impact between B and C , we cannot conserve kinetic energy of the entire system. The velocity of B immediately after collision is along unit vector

    A
    `hati`
    B
    `(hati+hatj)/sqrt(2)`
    C
    `(sqrt(3))/2hati+1/2hatj`
    D
    none of these

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    A
    `(mv_(0))/8`
    B
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    C
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    D
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