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BITSAT 2015 Paper

Section: Physics

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Question : 30 of 150

Marks: +1, -0

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii

R_1

R_2

, respectively. The ratio of masses of X and Y is

$\left(\frac{R_1}{R_2}\right)^{1/2}$
$\left(\frac{R_2}{R_1}\right)$
$\left(\frac{R_1}{R_2}\right)^2$
$\left(\frac{R_1}{R_2}\right)$

Solution:

When a charge particle is allowed to move in a uniform magnetic field, then it describes spiral or circular path

Centripetal force,

\frac{mv^2}{R}

= qvB

∴ v =

\left(\frac{qB}{m} R\right)

Hence,

\sqrt{\frac{2qV}{m}}

=

\left(\frac{qB}{m}\right)

R

\left[\text{Since } V = \sqrt{\frac{2qV}{m}}\right]

⇒ R =

\left(\frac{2mV}{q}\right)^{1/2}

×

\frac{1}{B}

or , m α

R^2

[Since V , q and B are constant]

or ,

\frac{m_1}{m_2}

=

\left(\frac{R_1}{R_2}\right)^2

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