BITSAT2016PhysicsElectrostaticsActual
Two identical charged spheres suspended from a common point by two massless strings of lengths I, are initially at a distance d ( d <<1) 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:
Options
- Av x^ 1 2
- Bv x
- Cv x^ - 1 2
- Dv x⁻¹
Correct answer
C. v x^ - 1 2
Step-by-step solution
From figure = F _ e mg kq ² x ² mg = x 2 or x³ q² (1) or x^ 3 / 2 q (2) Differentiating eq. (1) w.r.t. time 3 x ² dx dt 2 q dq dt but dq dt is constant so x ²( v ) q Replace q from eq. (2) x ²( v ) x ^ 3 / 2 or v x ^ -1 / 2