Two charged particles of masses m and 2m have charges +2q and +q respectively. They are kept in unif

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2. Electric Potential and Capacitance

hard

Two charged particles of masses $m$ and $2m$ have charges $+2q$ and $+q$ respectively. They are kept in uniform electric field and allowed to move for some time. The ratio of their kinetic energies will be

$1 : 1$

$4 : 1$

$1 : 4$

$8 : 1$

Solution

Accelerations of particles are

$a_{1}=\frac{2 q E}{m}$ and $a_{2}=\frac{q E}{2 m}$

Their final velocities after time $\mathrm{t},$

${\mathrm{v}=0+\mathrm{at}=\mathrm{at}} $

$\mathrm{v}_{1}=\frac{2 \mathrm{q} \mathrm{E}}{\mathrm{m}} \mathrm{t}$ and $\mathrm{v}_{2}=\frac{\mathrm{q} \mathrm{E}}{2 \mathrm{m}} \mathrm{t}$

Ratio of kinetic energy of the two particles

$\frac{\mathrm{K}_{1}}{\mathrm{K}_{2}}=\frac{\frac{1}{2} \mathrm{mv}_{1}^{2}}{\frac{1}{2} 2 \mathrm{mv}_{2}^{2}}=\frac{\mathrm{v}_{1}^{2}}{2 \mathrm{v}_{2}^{2}}=\frac{8}{1}$

Standard 12

Physics

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(AIPMT-2002)

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(AIIMS-2000)

Two charged particles of masses $m$ and $2m$ have charges $+2q$ and $+q$ respectively. They are kept in uniform electric field and allowed to move for some time. The ratio of their kinetic energies will be

Solution

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