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Two beads of masses m(1) and m(2) connec...

Two beads of masses `m_(1) and m_(2)` connected by an inextensible string are kept at rest at the horizontal diametrical points of a fixed smooth vertical semicircular tube. If the beads are released from the given position, find their speeds as the function of vertical distance y converted by miss `m_(2).`

Text Solution

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`sqrt((2gm_(2)y-m_(1)R sin((Y)/(R)))/(m_(1)+m_(2)))`
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Knowledge Check

  • Two beads A & B of equal mass m are connected by a light inextensible to move on a connected to move on a frictionless ring in vertical plane. The beads are released from rest as shown. The tension in the cord just after the release is:

    A
    `sqrt(2) mg`
    B
    `(mg)/2`
    C
    `(mg)/4`
    D
    `(mg)/sqrt(2)`

  • Two masses m_(1) and m_(2) are connected by light inextensible string passing over a smooth pulley P . If the pulley moves vertically upwards with an acceleration equal to g then .

    A
    Tension on the string is `(4m_(1)m_(2)g)/(m_(1)+m_(2))`
    B
    Tension on the string is `(2m_(1)m_(2)g)/(m_(1)+m_(2))`
    C
    The acceleration of mass `m_(1)` with respect to ground is `(3m_(2)-m_(1))/(m_(1)+m_(2))g` .
    D
    The acceleration of mass `m_(1)` with respect to ground is `(2(m_(2)-m))/(m_(1)+m_(2))g`

  • Beads A and B each of mass m , are connected by a light inextensible cord. They are constrained (restricted) to move on a frictionless ring in a vertical plane as shown. The beads are released from rest at the position shown. The tension in the cord just after the release is.

    A
    `sqrt(2)mg`
    B
    `mg`
    C
    `(mg)/(sqrt2)`
    D
    `2mg`

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