Question

A particle of mass $m$ and charge $q$ is fastened to one end of a string of length $l$, 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 $\sqrt{\frac{2qEI}{m}}$
• B. the speed of the particle when it reaches $B$ is $\sqrt{\frac{qEI}{m}}$
• C. the tension in the string when the particle reaches at $B$ is $qE$
• D. the tension in the string when the particle reaches at $B$ is zero

Answer 1

The correct option is B the speed of the particle when it reaches $B$ is $\sqrt{\frac{qEI}{m}}$

Using work-energy theorem:

$W_{all}=\Delta K.E$

$\overrightarrow{qE}.\overrightarrow{d}=\frac{1}{2}m{v}^2-0$

Note that displace in the direction of E is $l(1-cos\theta )$

$qEl(1-cos\theta )=\frac{1}{2}m{v}^2$

$\Rightarrow v=\sqrt{\frac{qEl}{m}}$