Two masses each equal to m are lying on X-axis at (- a,0) and (+ a, 0) respectively as shown in fig.
They are connected by a light string. A force F is applied at the origin and along the Y-axis. As a result, the masses move towards each other What is the acceleration of each mass ? Assume the instantaneous position of the masses as (- x,0) and {x, 0) respectively

Question

Two masses each equal to m are lying on X-axis at (- a,0) and (+ a, 0) respectively as shown in fig.

They are connected by a light string. A force F is applied at the origin and along the Y-axis. As a result, the masses move towards each other What is the acceleration of each mass ? Assume the instantaneous position of the masses as (- x,0) and {x, 0) respectively

Infinity Learn · Accepted Answer

See figure.From figure $$F=2Tcos$$⁡θ or $$T=F/(2cos$$⁡θ$$)The$$ force responsible for motion of masses on $$X-axis$$ is Tsin⁡θ∴ $$ma=Tsin$$⁡θ$$=F2cos$$⁡θ×$$sin$$⁡θ $$=F2tan$$⁡θ$$=F2$$×$$OBOA=F2$$×$$x(a2$$−$$x2)So$$, $$a=F2m$$×$$x(a2$$−$$x2)$$.

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