Two small balls A and B of positive charge Q each and masses m and 2m, respectively, are connected by a nonconducting 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)

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rod has angular acceleration QE/2 mL in clockwise direction

rod has angular acceleration QE/2mL in anticlockwise direction

acceleration of mass m is 2QE/3 m toward right

acceleration of mass m is QE/m toward right

answer is A.

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Detailed Solution

Resultant force on arrangement is 2QE,thus acceleration of center of mass is given by $a_{C} = 2 QE / 3 m$ .
Net torque on system about its centre of mass is
$QE (\frac{2 L}{3}) - QE (\frac{L}{3}) = [m \times \frac{4 L^{2}}{9} + 2 m \times \frac{L^{2}}{9}] α α = \frac{QE}{2 mL} (clock wise)$
From constraint equation, we get
$a_{A} = a_{C} + α (\frac{2 L}{3}) = \frac{2 QE}{3 m} + \frac{QE}{2 mL} (\frac{2 L}{3}) = \frac{3 QE}{3 m} = \frac{QE}{m}$