Two particles X and Y having equal charge, after being accelerate… - Vidyadip

Question

Two particles $X$ and $Y$ having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is:

✓

Answer

Particles $X$ and $Y$ of respective masses $m_1$ and $m_2$ are carrying charge q describing circular paths with respective radii $R_1$ and $R_2$ such that,$\text{R}_1=\frac{\text{m}_1\text{v}_1}{\text{qB}}$
$\text{R}_1=\frac{\text{m}_2\text{v}_2}{\text{qB}}$
Since both the particles are accelerated through the same potential difference, both will have the same kinetic energy.
$\therefore\frac{1}{2}\text{m}_1\text{v}_1^2=\frac{1}{2}\text{m}_2\text{v}_2^2$
$\because\text{R}_1=\frac{\text{m}_1\text{v}_1}{\text{qB}}$
$\Rightarrow\text{v}_1=\frac{\text{R}_1\text{qB}}{\text{m}_1}$
And,
$\text{R}_2=\frac{\text{m}_2\text{v}_2}{\text{qB}}$
$\Rightarrow\text{v}_2=\frac{\text{R}_2\text{qB}}{\text{m}_2}$
$\therefore\text{m}_1\Big(\frac{\text{R}_1\text{qB}}{\text{m}_1}\Big)^2=\text{m}_2\Big(\frac{\text{R}_2\text{qB}}{\text{m}_2}\Big)^2$
$\Rightarrow\frac{\text{m}_1}{\text{m}_2}=\frac{\text{R}_1^2}{\text{R}_2^2}=\Big(\frac{\text{R}_1}{\text{R}_2}\Big)^2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Moving Charges and Magnetism→Moving Charges and Magnetism — all question types→Physics STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Predict the effect of temperature of the conductor on the drift velocity of electrons.

Two coils X and Y are linked such that emf E is induced in Y when the current in X is changing at the rate $\text{I}\big(=\frac{\text{dI}}{\text{dt}}\big)$. If a current I0 is now made to flow through Y, the flux linked with X will be.

The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches 3.5R. The most appropriate reason for this behaviour is that at high temperatures:

Oxygen does not behave as an ideal gas.
Oxygen molecules dissociate in atoms.
The molecules collide more frequently.
Molecular vibrations gradually become effective.

In image formation from spherical mirrors, only paraxial rays are considered because they:

Boron rods in a nuclear reactor are used to:

In n-type of semiconductor, majority carries are:

If the dipole with charges $\pm q$ are kept perpendicular to each other inside a closed cube, then the total electric flux emerging out of the cube will be:

As the electron in Bohr orbit of Hydrogen atom passes from state n = 2 to n = 1, the kinetic energy K and potential energy U change as(a) K two-fold, U four-fold(b) K four-fold, U two-fold(c) K four-fold, U also four-fold (d) K two-fold, U also two-fold

Assertion : If different gases are filled turn by turn at the same pressure in the discharge tube the discharge in them takes place at the same potential.
Reason : The discharge depends only on the pressure of discharge tube and not on the ionisation potential of gas.(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.(c) If assertion is true but reason is false.(d) If the assertion and reason both are false.

The minimum frequency $v$ of continuous $X-$rays is related to the applied potential difference $V$ as