NEET | 2016Center of MassHard

Question

Two identical charged spheres suspended from a common point by two massless strings of lengths 𝑙, areinitially at a distance d(d< < 𝑙) apart because of their mutual repulsion. The charges begin to leak fromboth the spheres at a constant rate. As a result, the spheres approach each other with a velocity υ. Then υvaries as a function of the distance 𝑥 between the spheres, as

Options

A.

υ ∝ x12

B.

υ∝x

C.

υ∝ x-12

D.

υ ∝x-1

Solution


θ=x2l
fe cos θ = mgh λθ
fe = mg. (x/2)
kq2x2=mgx2e
kq2 = mg2lx3
q ∝ x32
dqdt∝32x12.dxdt
⇒ x12. v = constant
v∝ x-12

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