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Two identical small masses each of mass ...

Two identical small masses each of mass m are connected by a light inextensible string on a smooth horizontal floor. A constant force F is applied at the mid point of the string as shown in fig. find the acceleration of each mass towards each other.

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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