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# Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance  d(d<<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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a
v∝x-1/2
b
v∝x-1
c
y∝x1/2
d
v∝x

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detailed solution

Correct option is A

From figure, Tcosθ=mg…..(i)Tsinθ=kq2x2……..(ii) From eqns. (i) and (ii), tanθ=kq2x2mg Since θ is small, ∴tanθ=sinθ=x2l ∴x2l=kq2x2mg⇒q2=x3mg2lk or q∝x3/2⇒dqdt∝32xdxdt=32xv. Since, dqdt= constant ∴v∝1x

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