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Physics Question on centripetal acceleration

An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

A

√2:1

B

2√2:1

C

4√2:1

D

8:1

Answer

2√2:1

Explanation

Solution

The ratio of linear momenta acquired by above two particles,
pαpp=2(4m)(2eV)2(m)(eV)\frac{pα}{pp}=\frac{\sqrt{2(4m)(2eV)}}{{\sqrt{2(m)(eV)}}}
=16√2=\frac{\sqrt{16}}{√2}
=4√2\frac{4}{√2}
=2√21=\frac{2√2}{1}
So, the correct option is (B): 2√21\frac{2√2}{1}