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A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \mathrm{r_{d}}  and \mathrm{r_{p}} are the radii of their circular paths respectively, then the ratio \mathrm{\frac{r_{d}}{r_{p}}} will be \mathrm{\sqrt{x}: 1} where \mathrm{x} is ________.

Option: 1

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Option: 2

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Option: 3

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Option: 4

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\mathrm{r= \frac{mV}{qB}= \sqrt{\frac{2mK}{qB}}}
If kinetic energy is the same
\mathrm{r \propto \: \sqrt{\frac{m}{q}}}
\mathrm{\frac{r_{d}}{r_{p}}= \frac{\sqrt{\frac{m_{d}}{q_{d}}}}{\sqrt{\frac{m_{p}}{q_{p}}}}= \sqrt{\frac{m_{d}}{m_{p}}}\times \sqrt{\frac{q_{p}}{q_{d}}} }
       \mathrm{= \sqrt{\frac{2}{1}}\times \sqrt{\frac{1}{1}}= \sqrt{2}:1 }

Ans : (2)

Posted by

Pankaj Sanodiya

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