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Two particles of mass 'm' each are tied ...

Two particles of mass 'm' each are tied at eh ends of a light string of length '2a' The whole system is kept on frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' from the centre P (as shown in figure). Now the mid point of the string is pulled vertically upwards with a small but constant force F As a result, the particles move towards each other on the surface the magnitude of acceleration, when the separation between them becomes 2x is:

A

`F/(2m)a/sqrt(a^(2)-x^(2))`

B

`F/(2m)x/sqrt(a^(2)-x^(2))`

C

`F/(2m)x/a`

D

`F/(2m)sqrt((a^(2)-x^(2))/x)`

Text Solution

Verified by Experts

The correct Answer is:
B
From the figure

`F=2T sin theta` ….(i)
`mA=T cos theta` ….(ii)
Dividing eqn (ii) by eqn (i)
`(cos theta)/(2sin theta)=(mA)/F`
`A=F/(2m)cottheta=F/(2m)x/sqrt(a^(2)-x^(2))`
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Knowledge Check

  • Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance a from the centre P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is

    A
    `(F)/(2m) /(sqrt(a^2-x^2))`
    B
    `(F)/(2m)(x)/(sqrt(a^2-x^2))`
    C
    `(F)/(2m)(x)/(a)`
    D
    `(F)/(2m)(sqrt(a^2-x^2))/(x)`

  • Two particles of mass m each are tied at the ends of a light string of length 2a . The whole system is kept on a frictionless horizontal surface with the string held tight so that, each mass is at a distance 'a' from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x , is :

    A
    `(F)/(2m)(a)/(sqrt(a^(2)-x^(2)))`
    B
    `(F)/(2m)(x)/(sqrt(a^(2)-x^(2)))`
    C
    `(F)/(2m)(x)/(a)`
    D
    `(F)/(2m)(sqrt(a^(2)-x^(2)))/(x)`

  • Two masses M and m are connected by a weightless string. They are pulled by a force F on a frictionless horizontal surface. The tension in the string will be

    A
    `(FM)/(m+M)`
    B
    `(F)/(M+m)`
    C
    `(FM)/(m)`
    D
    `(Fm)/(M+m)`

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