The velocity of a body of rest mass m₀ is c √3/2 (where c is the velocity of light in vacuum). Then mass of this body is

The correct answer is 2m₀.

This problem is based on Einstein's Special Theory of Relativity. When a body moves at a speed comparable to the speed of light, its relativistic mass increases according to the relativistic mass formula:

m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}

where m₀ is the rest mass, v is the velocity of the body, and c is the speed of light in vacuum.

Step 1: Identify the given velocity.

The velocity of the body is given as:

v=c\frac{\sqrt{3}}{2}

Step 2: Calculate v²/c².

Square the velocity:

v^2=c^2\times \frac{3}{4}

Therefore:

\frac{v^2}{c^2}=\frac{3}{4}

Step 3: Evaluate the term inside the square root.

1-\frac{v^2}{c^2}=1-\frac{3}{4}=\frac{1}{4}

Step 4: Take the square root.

\sqrt{1-\frac{v^2}{c^2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}

Step 5: Substitute back into the relativistic mass formula.

m=\frac{m_0}{\frac{1}{2}}=m_0��2=2m_0

Conclusion: When a body of rest mass m₀ travels at a speed of c\frac{\sqrt{3}}{2}, its relativistic (observed) mass becomes 2m₀ — exactly double its rest mass. This beautifully illustrates how mass increases with velocity in special relativity, approaching infinity as speed approaches c.