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

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)(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
The arrangement is shown in the figure. The separation between the two masses is 2x. Each mass will move in the horizontal direction as shown in the figure.
Let the tension in the string be T. The forces acting t point P and on one of the masses are shown in the figure. Net force at point P must equal zero.
`therefore 2Tsin =F...(i) `
Also, for the mass m,
`N+T sin theta-mg=0 ....(ii)`
and `T cos theta=mA....(iii)`
Equations (i) and (iii) give `A=(F cot theta)/(2m)=(F)/(2m)((x)/(sqrt(a^(2)-x^(2))))`
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Knowledge Check

  • 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)`

  • 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

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    C
    `( g)/( 5)`
    D
    `( g)/( 10) `

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