Two small balls A and B of positive charge Q each and masses m and 2m, respectively, are connected by a non conducting light rod of length L. This system is released in a uniform electric field of strength E as shown. Just after the release (assume no other force acts on the system)

Options

A. rod has angular acceleration `QE//2mL` in anticlockwise direction.
B. rod has angular acceleration `QE//2mL` in anticlockwise direction
C. acceleration of point A is `2QE//3m` toward right
D. acceleration of point A is `QE//m` toward right .

Answer

A, D

Explanation

a.,d.
Resultant force on arrangement is `2QE`, thus acceleration of center of mass is given by `a_(c)=2QE//3m`.
Net torque on system is
`QE((2L)/(3))=QE((L)/(3))=[mxx(4L^(2))/(9)+2mxx(L^(2))/(9)]a`
`a=(QE)/(2mL` (clockwise)
From constraint equation, we get
`a_(A)=a_(c)+a((2L)/(3))`
`=(2QE)/(3m)+(QE)/(2mL)((2L)/(3))=(3QE)/(3m)=(QE)/(m)`