Question

Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii r₁ and r₂ respectively. The ratio of the mass of X to that of Y is ______.

पर्याय

• `"r"_1/"r"_2`

• `sqrt("r"_1/"r"_2)`

• `["r"_2/"r"_1]^2`

• `["r"_1/"r"_2]^2`

Answer 1

Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii r₁ and r₂ respectively. The ratio of the mass of X to that of Y is `underlinebb("r"_1/"r"_2)`.

Explanation:

Force acting on the particle inside magnetic field

F_B = qvB sinθ

This force F_B provides necessary centripetal force `"mv"^2/"r"` for circular motion of the charged particle

∴ `"mv"^2/"r"` = qvB sinθ 

Now, for particles x and y and for θ = 90°

`("m"_x"v"_x^2)/"r"_1` = qv_xB            ...(i)

`("m"_"y""v"_"y"^2)/"r"_2` = qv_yB            ...(ii)

From eqs. (i) and (ii)

`("m"_x"v"_x)/("m"_"y""v"_"y")="r"_1/"r"_2`

⇒ `"m"_x/"m"_"y"="r"_1/"r"_2`       [∵ `"v"_x/"v"_"y"=1`]