Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d(d less than 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 [NEET-2016]

Question : (NEET 2016)

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 [NEET-2016]

Options :

(1) v ∝ x^(-1)
(2) v ∝ x^(1/2)
(3) v ∝ x
(4) v ∝ x^(-1/2)

Answer : (4) v ∝ x^(-1/2)

Solution :

Figure is prepared based on given data in question which is shown below. 

To find velocity, we have to differentiate it with respect to time. So dx/dt will be velocity. 

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