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The particle P of mass m is attached to ...

The particle P of mass m is attached to two light, rigid rods AP and BP of length l each. A and B are hings on a fixed vertical axis. The system APB can rotate freely about this axis. The angle ABP = the angle `BAP = theta`. The tensions in AP and BP are `T_(1)` and `T_(2)` respectively.

When the system is at rest, which of the following is not correct?

A

At P, the direction of `T_(1)` is from P to A.

B

At P, the direction of `T_(2)` is from P to B.

C

The rods AP and BP together exert a net force and net torque on AB.

D

`T_(1) = T_(2)`.

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The particle P of mass m is attached to two light, rigid rods AP and BP of length l each. A and B are hings on a fixed vertical axis. The system APB can rotate freely about this axis. The angle ABP = the angle BAP = theta . The tensions in AP and BP are T_(1) and T_(2) respectively. When the system is made to rotate about AB with angular velocity omega , which of the following is not correct?

    A
    `T_(1)` will always be greater than `T_(2)`.
    B
    `T_(1) - T_(2) = momega^(2)t` for small values of `omega`.
    C
    `T_(2)` will become zero for `omega^(2) = g//l cos theta`.
    D
    The direction of `T_(2)` will always be from P to B.

  • The particle P of mass m is attached to two light, rigid rods AP and BP of length l each. A and B are hings on a fixed vertical axis. The system APB can rotate freely about this axis. The angle ABP = the angle BAP = theta . The tensions in AP and BP are T_(1) and T_(2) respectively. The system is now rotated by 90^(@) so that must be imparted to P, normal to the plane of the figure, such that it moves in a complete circular path in a vertical plane with AB as the axis?

    A
    `2sqrt(gl sin theta)`
    B
    `2sqrt(gl cos theta)`
    C
    `(5//2)sqrt(gl sin theta)`
    D
    None of these

  • A particle P of mass m is attached to a vertical axis by two strings AP and BP of legth l each. The separation AB=l , rotates around the axis with an angular velocity omega . The tension in the two string are T_(1) and T_(2) . Then

    A
    `T_(1)=T_(2)`
    B
    `T_(1)+T_(2)=m omega^(2)l`
    C
    `T_(1)-T_(2)=2mg`
    D
    `BP` will remains taut only if `omega ge sqrt(2g//l)`

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