Question

Two masses each equal to m are lying on x-axis at (-a, 0) and (+ a, 0) respectively. They are connected by a light string. A force F is applied at the origin along y axis resulting into motion of masses towards each other. The acceleration of each mass when position of masses at any instant becomes (- x, 0) and (+ x, 0) is given by

• A. $\frac{F}{m}\frac{x}{\sqrt{a^{2} - x^{2}}}$
• B. $\frac{F}{m}\frac{\sqrt{a^{2} - x^{2}}}{x}$
• C. $\frac{Fx}{2m\sqrt{a^{2} - x^{2}}}$
• D. $\sqrt{\frac{a^{2} - x^{2}}{x}}$

Answer 1

Answer: (C)

$\frac{Fx}{2m\sqrt{a^{2} - x^{2}}}$

Answer 2

Let F be applied at origin from figure

F = 2T cos θ

or T = F/2cosθ

Then force causing motion is given by T

T sin θ = $\left( \frac{F}{2\cos\theta} \right)\sin\theta$

= $\frac{F}{2}\tan\theta = \frac{F}{2}\frac{x}{\sqrt{a^{2} - x^{2}}}$

∴ acceleration = $\frac{F}{2m}.\frac{x}{\sqrt{a^{2} - x^{2}}}$