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Two lead balls of mass m and 2 m are pla...

Two lead balls of mass m and 2 m are placed at a separation d. A third ball of mass m is placed at an unknown location on the line joining the first two balls such that the net gravitational force experienced by the first ball is `(6Gm^(2))/(d^(2)` . What is the location of the third ball?

Text Solution

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The correct Answer is:
Exactly midway between the two balls OR at a dietance of `(d)/(2sqrt(2))` form the ball of mass m
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Knowledge Check

  • Two point masses m and 4 m are seperated by a distance d on a line . A third point mass m_(0) is to be placed at a point on the line such that the net gravitational force on it zero . The distance of that point from the m mass is

    A
    `d/2`
    B
    `d/4`
    C
    `d/3`
    D
    `d/5`

  • A ball of mass m_(1) , collides elastically and head on with ball of mass m_(2) at rest. Then

    A
    The transfer of kinetic energy to the second ball is maximum when `m_(1) = m_(2)`
    B
    The change of momentum of first ball is maximum, when `m_(1) lt lt m_(2)`.
    C
    The velocity of the second ball is maximum, when `m_(1) gt gt m_(2)`.
    D
    None of these

  • Two ivory balls are placed together at rest. A third identical ball moving with velocity u in the line of first two balls, as shown in figure collide head on elastically then

    A
    Thrid ball comes to rest with second ball while first ball moves with speed u
    B
    Third ball comes to rest and other two move together with speed `(u)/(2)`
    C
    All three ball move together with speed `(u)/(3)`
    D
    All three ball move in such a manner each makes angle `120^(@)` to each other

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