Assertion :A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal. Reason: Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\to B$ in a direction perpendicular to $\to B$ , will describe circular trajectories of equal radii.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
The radius of the circular path is given by $r = \frac{m v}{q B} = \frac{\sqrt{2 m K}}{q B}$ ; where $K = \frac{1}{2} m v^{2}$

Since $K$ and $B$ are the same for the two particles, $r \propto \frac{\sqrt{m}}{q}$ .

Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, $\sqrt{m} / q$ will be same for both particles.
Hence, $r$ will be the same for both particles.

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Similar questions

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

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

Choose the most appropriate correct option:

Assertion (A) All collision of reactant molecules lead to product formation.

Reason (R) Only those collisions in which molecules have correct orientation and sufficient kinetic energy lead to compound formation.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

Q. Assertion: Average kinetic energy in one oscillation during

SHM

of a body is

\frac{1}{4} m ω^{2} A^{2}

.
Reason: Maximum kinetic energy is

\frac{1}{2} m ω^{2} A^{2}

Assertion: Be and Al have similar properties.

Reason: $B e^{2 +}$ and $A l^{3 +}$ have nearly the same charge/volume ratios and similar polarising power.

Q. Assertion : Two electrons of helium atom are placed in only one shell but three electrons of lithium need two shells.
Reason: A shell can have maximum

{2n}^{2}

electrons.

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