Question

Assertion :If a proton and an $\alpha$-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of $\alpha$-particle is double than that of proton. Reason: In a magnetic field, the period of revolution of a charged particle is directly proportional to the mass of the particle and inversely proportional to the charge of particle.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

From the expression $T=\frac{2\pi m}{qB}$

$T_{\alpha }=\frac{2\pi m_{\alpha }}{q_{\alpha }B}$

$T_p=\frac{2\pi m_p}{q_{p}B}$

$\frac{T_{\alpha }}{T_p}=\frac{m_{\alpha }}{m_p}\times \frac{q_p}{q_{\alpha }}=4\times \frac{1}{2}=2$