Given below are two statements labelled as Assertion (A) and Reason (R

1.	Given below are two statements labelled as Assertion (A) and Reason (R)Assertion(A): A proton and an electron, with same momenta, enter in a magnetic field in a direction at right angles to the lines of the force. The radius of the paths followed by them will be same.Reason(R): Electron has less mass than the proton.Select the most appropriate answer from the options given below: (i) Both A and R are true and R is the correct explanation of A (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) A is false and R is also false.
Answer» Answer is (ii) Both A and R are true but R is not the correct explanation of A. we know \(\frac{mv^2}{r}\) = Bqvsin θ = Bqv sin θ Centripetal force = magnetic Lorentz force sin θ = sin 90^θ = 1 (∠ between \(\overrightarrow{V}\) & \(\overrightarrow{B}\) = 90°) \(\frac{mv^2}{r}\) = Bqv \(\frac{mv}{r}\) = Bq \(r=\frac{mv}{Bq}=\frac{p}{Bq}=\frac{linear\,momentum}{Bq}\) Since = \(\frac{p}{Bq}\) Given p, B are same Also q for proton & electron is same except its sign ∴ Radius is same. So statement is correct but reason is not the correct explanation of the given assertion.

Given below are two statements labelled as Assertion (A) and Reason (R)Assertion(A): A proton and an electron, with same momenta, enter in a magnetic field in a direction at right angles to the lines of the force. The radius of the paths followed by them will be same.Reason(R): Electron has less mass than the proton.Select the most appropriate answer from the options given below: (i) Both A and R are true and R is the correct explanation of A (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) A is false and R is also false.

Answer»

Answer is (ii) Both A and R are true but R is not the correct explanation of A.

we know \(\frac{mv^2}{r}\) = Bqvsin θ = Bqv sin θ

Centripetal force = magnetic Lorentz force

sin θ = sin 90^θ = 1 (∠ between \(\overrightarrow{V}\) & \(\overrightarrow{B}\) = 90°)

\(\frac{mv^2}{r}\) = Bqv

\(\frac{mv}{r}\) = Bq

\(r=\frac{mv}{Bq}=\frac{p}{Bq}=\frac{linear\,momentum}{Bq}\)

Since = \(\frac{p}{Bq}\)

Given p, B are same

Also q for proton & electron is same except its sign

∴ Radius is same. So statement is correct but

reason is not the correct explanation of the given assertion.