Q135 / 155 · WBJEE 2020 · Physics

Four identical point masses, each of mass $\mathrm{m}$ and carrying charge $+\mathrm{q}$ are placed at the corners of a square of sides 'a' on a frictionless plain surface. If the particles are released simultaneously, the kinetic energy of the system when they are infinitely far apart is

  • A
    $\frac{q^{2}}{a}(2 \sqrt{2}+1) \times \mathrm{k}$
  • B
    $\frac{\mathrm{q}^{2}}{\mathrm{a}}(\sqrt{2}+2) \times \mathrm{k}$
  • Correct answer
    C
    $\frac{q^{2}}{a}(\sqrt{2}+4) \times \mathrm{k}$
  • D
    $\frac{q^{2}}{a}(\sqrt{2}+1) \times \mathrm{k}$

Solution

Hint: Hint $: \mathrm{KE}_{i}+\mathrm{PE}_{\mathrm{i}}=\mathrm{KE}_{\mathrm{f}}+\mathrm{PE}_{\mathrm{f}}$ $\therefore \mathrm{KE}_{\mathrm{t}}=\mathrm{PE}_{i}=4 \frac{\mathrm{Kq}^{2}}{\mathrm{a}}+2 \frac{\mathrm{Kq}^{2}}{\sqrt{2} \mathrm{a}}=\frac{\mathrm{Kq}^{2}}{\mathrm{a}}(4+\sqrt{2}), \mathrm{K}=1$ in C.G.S. unit

Hence, the correct answer is option: 'C'.

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