Question

A particle of mass m and charge q is fastened to one end of a light string of length $\ell$. The other end of the string is fixed to the point O. The whole system lies on a frictionless horizontal plane. Initially, the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then :

• A. the speed of the particle when it reaches B is $\sqrt{\frac{2qEl}{m}}$
• B. the speed of the particle when it reaches B is $\sqrt{\frac{qEl}{m}}$
• C. the tension in the string when particles reaches at B is 2qE
• D. the tension in the string when the particle reaches at B is zero

Answer 1

Answer: (B), (C)

the speed of the particle when it reaches B is $\sqrt{\frac{qEl}{m}}$
the tension in the string when particles reaches at B is 2qE

The work done by the tension of string is zero. Since there is no friction, only electric field does work.
$qEl(1-cos{60}^{\circ })=1/2m{u}^2$
$u=\sqrt{qEl/m}$
At B, the tension in the string is responsible for centripetal acceleration,
$T-qE=m{v}^2/L=qE\Rightarrow T=2qE$