Question

• The fractional increase of mass of a particle for velocity 0.1 c is----- Answer A. O 0.005 B. O 0.007 C. O 0.008 D. O 0.009​

Answer 1

To find: The equation for calculating the fractional increase in mass of the particle for a given velocity of 0.1c.
Solution:
m = m0/[1-v^2/c^2]^1/2
(m0 = the rest mass)
(m = the mass of particle)
(v = the speed of the particle)
(c = the speed of light)
let v/c goes to higher value,
the 1-v^2/c^2 goes less.
If v=0.1 c so( 0.1 c)^2/c^2)=0.01
[1–0.01]^1/2=[0.99]^1/2 =[99}^1/2/10=~ 0.94 M=m(1/0.95)=(100/95) m
M>m(1.005)=1.005 m.
Therefore the increase in the mass at speed (0.1 c) is about 0.005 m.
Hence, the correct answer is option (A) i.e 0.005
#SPJ3

Answer 2

Answer:

The fractional increase of mass of a particle for velocity 0.1c is A. 0.005

Explanation:

Given:

velocity(v) = 0.1c

To find:

Increase in the mass =?

Formula:

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

Solution:

In the given formula, m is the mass of the particle, m₀ is the rest mass of the particle, v is the velocity of the particle, and c is the velocity of light.

Substituting the given values in the above-mentioned formula, we get

$m = \frac{m_0}{\sqrt{1-\frac{(0.1c)^2}{c^2}} }$

$m = \frac{m_0}{\sqrt{1-\frac{0.01c^2}{c^2}} }$

$m = \frac{m_0}{\sqrt{1-0.01} }$

$m = \frac{m_0}{\sqrt{0.99} }$

$m = \frac{m_0}{0.995}$

m = 1.005m₀

Increase in mass = m - m₀

Increase in mass = 1.005m₀ - m₀

Increase in mass = 0.005m₀

Therefore, the increase in mass of a particle at 0.1c is 0.005

#SPJ1