Question

Assertion: A proton and an $\alpha$ - particle are projected with the same kinetic energy at right angle to a uniform magnetic field, then the $\alpha$ - particle will move along a circular path of smaller radius than the proton.

Reason : $Bqv=\frac{m{v}^2}{r}$ holds good for the charged particle moving in a circular path in a uniform magnetic field.

Choose the most appropriate correct option:

• A. Assertion is false but Reason is true.
• B. Assertion is true but Reason is false.
• C. Both Assertion and Reason are true but Reason is not the correct explanation of assertion.
• D. Both Assertion and Reason are true and Reason is correct explanation of Assertion.

Answer 1

The correct option is A

Assertion is false but Reason is true.

$E=\frac{1}{2}m{v}^2$ or $v=\sqrt{\frac{2E}{m}}$

$Bqv=\frac{m{v}^2}{r}$

Or $r=\frac{mv}{Bq}=\frac{m}{Bq}\sqrt{\frac{2E}{m}}=\sqrt{\frac{2mE}{Bq}}$

i.e., $r\propto \frac{\sqrt{m}}{q}$

$\therefore \frac{r_p}{r\alpha }=\sqrt{\frac{m_p}{m_{\alpha }}}\times \frac{q_{\alpha }}{q_p}=\sqrt{\frac{1}{4}}\times \frac{2}{1}=1$

i.e., radius of both the particles should be same. Hence statement : 1 is wrong and statement : 2 is correct.