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Question: The velocity of a body of rest mass \(m_{0}\) is \(\frac{\sqrt{3}}{2}c\) (where c is the velocity of...

The velocity of a body of rest mass m0m_{0} is 32c\frac{\sqrt{3}}{2}c (where c is the velocity of light in vacuum). Then mass of this body is

A

(3/2)m0(\sqrt{3}/2)m_{0}

B

(1/2)m0(1/2)m_{0}

C

2m02m_{0}

D

(2/3)m0(2/\sqrt{3})m_{0}

Answer

2m02m_{0}

Explanation

Solution

From Einstein’s formula

m=m01−v2c2=m01−(32C)2C2m = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{m_{0}}{\sqrt{1 - \frac{\left( \sqrt{\frac{3}{2}}C \right)^{2}}{C^{2}}}} =m01−34=2m0= \frac{m_{0}}{\sqrt{1 - \frac{3}{4}}} = 2m_{0}