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Physics · PYQ NEET UG 2016(1)
हिन्दीTwo identical charged spheres suspended from a common point by two massless strings of lengths \( l \), are initially at a distance \( d (d \ll l) \) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity \( v \). Then \( v \) varies as a function of the distance \( x \) between the spheres, as
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Correct answer · Option C
\( v \propto x^{-\frac{1}{2}} \)
Explanation
Equilibrium condition: \( \frac{kq^2}{x^2} = mg \frac{x}{l} \implies q^2 \propto x^3 \implies q \propto x^{3/2} \). Differentiating with respect to time \( t \), \( \frac{dq}{dt} \propto x^{1/2} v \). Since \( \frac{dq}{dt} \) is constant, \( v \propto x^{-1/2} \).
