devarshi-dt-logo

Question:

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d (d<<l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result, the charges approach each other with a velocity v. Then as a function of distance x between them:

v∝x³/²

v∝x²

v∝x

v∝x½

Solution:

Tsinθ=Kq2x2(i)Tcosθ=mg (ii)ortanθ=Kq2x2mg=xl(from the FBD); sinced>>lorx3=Kq2ℓmg(...iii)x3∝q23x2dxdt∝2qdqdtx2⋅v∝qSubstituting the value ofqfrom equation (iii).v∝x𕒵2