Question

A ball of mass $5g$ and charge ${10}^{-7}C$ moves from point A whose potential is $500V$ to a point B whose potential is zero. The velocity of the ball at the point B, if its velocity at the point A is zero, is

• A. $0.1414cm{s}^{-1}$
• B. $0.1414m{s}^{-1}$
• C. $1.414cm{s}^{-1}$
• D. $1.414m{s}^{-1}$

Answer 1

Answer: (B)

$0.1414m{s}^{-1}$

Work done in moving the charge from point A to B is equal to change in its Kinetic Energy.

By law of consevation of energy
$q\left(\Delta V\right)=\frac{1}{2}mV{}^2$
$\Rightarrow {10}^{-7}\times 500=\frac{1}{2}\times (5\times {10}^{-3})V^2$

$\Rightarrow \frac{2\times {10}^{-5}}{{10}^{-3}}=V^2$

$\Rightarrow 2\times {10}^{-2}=V^2$
$\Rightarrow V=\sqrt{2}\times {10}^{-1}$
$\Rightarrow V=0.1414m{s}^{-1}$