Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describe circular paths of radii ? and ? respectively. The mass ratio of X and

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Q.
Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is [2024]

1 $(\frac{R_{1}}{R_{2}})$

2 ${(\frac{R_{2}}{R_{1}})}^{2}$

3 $(\frac{R_{2}}{R_{1}})$

4 ${(\frac{R_{1}}{R_{2}})}^{2}$

Ans.
(4)

$R = \frac{m v}{q B} = \frac{p}{q B} = \frac{\sqrt{2 m (KE)}}{q B} = \frac{\sqrt{2 m q V}}{q B}$

$R \propto \sqrt{m} \Rightarrow m \propto R^{2}$

$\frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}$

Solution

Q.
Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is [2024]

1 $(\frac{R_{1}}{R_{2}})$

2 ${(\frac{R_{2}}{R_{1}})}^{2}$

3 $(\frac{R_{2}}{R_{1}})$

4 ${(\frac{R_{1}}{R_{2}})}^{2}$

Ans.
(4)

$R = \frac{m v}{q B} = \frac{p}{q B} = \frac{\sqrt{2 m (KE)}}{q B} = \frac{\sqrt{2 m q V}}{q B}$

$R \propto \sqrt{m} \Rightarrow m \propto R^{2}$

$\frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}$

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Solution

Q. Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii R1 and R2 respectively. The mass ratio of X and Y is [2024]

1 (R1R2)

2 (R2R1)2

3 (R2R1)

4 (R1R2)2

Ans. (4) R=mvqB=pqB=2m(KE)qB=2mqVqB R∝m⇒m∝R2 m1m2=(R1R2)2

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Q.
Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is [2024]

1 $(\frac{R_{1}}{R_{2}})$

2 ${(\frac{R_{2}}{R_{1}})}^{2}$

3 $(\frac{R_{2}}{R_{1}})$

4 ${(\frac{R_{1}}{R_{2}})}^{2}$

Ans.
(4)

$R = \frac{m v}{q B} = \frac{p}{q B} = \frac{\sqrt{2 m (KE)}}{q B} = \frac{\sqrt{2 m q V}}{q B}$

$R \propto \sqrt{m} \Rightarrow m \propto R^{2}$

$\frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}$