Two particle of mass $m$ each are tied at the ends of a light string of length $2 \mathrm{a}$. 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 $\mathrm{P}$ (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 $2 \mathrm{x}$ is
Two particle of mass $m$ each are tied at the ends of a light string of length $2 \mathrm{a}$. 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 $\mathrm{P}$ (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 $2 \mathrm{x}$ is
- [IIT 2007]
- A
$\frac{F}{2 m} \frac{a}{\sqrt{a^2-x^2}}$
- B
$\frac{F}{2 m} \frac{x}{\sqrt{a^2-x^2}}$
- C
$\frac{F}{2 m} \frac{x}{a}$
- D
$\frac{F}{2 m} \frac{\sqrt{a^2-x^2}}{x}$
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