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Question

When a charged particle of charge x C moves through a potential difference of y V, the gain in kinetic energy is equal to xy J.
An electron and an alpha particle have their masses in the ratio of 1 : 7200 and charges in the ratio of 1 : 2. If they start moving from rest through the same electrical potential difference then the ratio of their velocities will be ______.

A
1 : 60
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B
60 : 1
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C
1 : 20
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D
20 : 1
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Solution

The correct option is B 60 : 1

Given : If particle has charge x coulombs and potential difference y volts . Then gain in K.E. = xy joules.

Using similar analysis,

(mass)electron(mass) alpha particle=17200

(charge)electron(charge) alpha particle=12

We need to find (velocity)electron(velocity) \alpha particle

Since initially there at rest, initial K.E. = 0;

They move through same potential difference. Let potential difference be y volts.

So, gain in K.E = Final K.E – Initial K.E

= Final K.E – 0

So, gain in K.E = charge×potentialdifference

Ratio of gain in K.E of electron and α particle = Ratio of final K.E of electron and α particle

12mv2e×y12mv2α×y

=12×7200=3600

vevα=3600=60


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