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
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
$\frac{F}{{2m}}\,\frac{a}{{\sqrt {{a^2} - {x^2}} }}$
- B
$\frac{F}{{2m}}\,\frac{x}{{\sqrt {{a^2} - {x^2}} }}$
- C
$\frac{F}{{2m}}\,\frac{x}{a}$
- D
$\frac{F}{{2m}}\,\frac{{\sqrt {{a^2} - {x^2}} }}{x}$
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Give the magnitude and direction of the net force acting on
$(a)$ a drop of rain falling down with a constant speed,
$(b)$ a cork of mass $10\; g$ floating on water,
$(c)$ a kite skillfully held stationary in the sky,
$(d)$ a car moving with a constant velocity of $30\; km/h$ on a rough road,
$(e)$ a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
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