A positively charged particle \(+q\) is projected with speed \(v\) toward a fixed charge \(+Q,\) and rebounds after reaching a minimum distance \(r.\) What will be the new closest distance of approach if its initial velocity is doubled to \(2v\text{?}\)

1. \(\dfrac{r}{4}\) 2. \(\dfrac{r}{2}\)
3. \(\dfrac{r}{16}\) 4. \(\dfrac{r}{8}\)
Subtopic:  Electric Potential Energy |
 72%
Level 2: 60%+
NEET - 2022
Hints

Six charges \(+q,\) \(-q,\) \(+q,\) \(-q,\) \(+q\) and \(-q\) are fixed at the corners of a hexagon of side \(d\) as shown in the figure. The work done in bringing a charge \(q_0\) to the centre of the hexagon from infinity is: (\(\varepsilon_0\text-\)permittivity of free space)
1. zero 2. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\)
3. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)\) 4. \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\)
Subtopic:  Electric Potential Energy |
 85%
Level 1: 80%+
NEET - 2022
Hints