Question

At what speed a particle moves if its mass is equal
to 4 times its rest mass
2.910 m/sec
1.9 ~ 108 m/sec
2.9x10 m/sec
2.9 x 108 cm/sec​

Answer 1

Answer:

Answer: c option 2.9×10m/hskks

Answer 2

Given:

A particle with mass = 4 X Its rest mass

To Find:

The speed of the particle

Solution:

The speed of the particle is 2.90 X 10⁸m/s.

The rest mass is the mass of the body when it is not in motion. As the body starts attaining a velocity, its mass slightly increases. This is called the relativistic mass.

The formula for relativistic mass is:

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

Here, m = Relativistic mass

mo = Rest mass

v = Velocity of the object

c = Speed of light in vaccum = 3 X 10⁸ m/s

According to the question,

m = 4mo

Substituting in the formula,

$4mo = \frac{mo}{\sqrt{1-\frac{v^2}{9X10^1^6} } }$

or 4 X $\sqrt{1-\frac{v^2}{9X10^1^6} }$ = 1

Squaring both the sides,

16 X (9 X 10¹⁶ - v² / 9 X 10¹⁶) = 1

or 9 X 10¹⁶ - v² = 9 X 10¹⁶/16

= 5.625 x 10¹⁵

or v² = 9 X 10¹⁶ - 5.625 x 10¹⁵

= 10¹⁶ (9 - 0.5625)

= 8.44 X 10¹⁶

Taking square root on both the sides,

v = 2.90 X 10⁸m/s