NEET-XII-Physics

exam-1 year:2016

with Solutions -
  • #9
    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 :
    (1)V ``\propto `` ``X^{\frac 12}``
    (2)V ``\propto `` X
    (3)V ``\propto `` ``X^{-\frac 12}``
    (4) V ``\propto `` ``X^{-1}``
    digAnsr:   3
    Ans : (3)
    Sol. tan = e
    F
    mg
    
    2
    2
    Kq x
    2x mg
    =



    x
    q q
    or 3 2x q ..... (1)
    or x3/2  q .... (2)
    differentiate eq.(i) w.r.t. time
    3x2
    dx
    dt
     2q
    dq
    dt
    but
    dq
    dt
    is constant
    so x2(v)  q replace q from eq. (2)
    x2(v)  x3/2 or 1/ 2v x