Question

A golf ball has a mass of 120g. Calculate its increase in mass when it is travelling at 40ms1. What is this as a percentage of its rest mass?

Answer 1

Answer:

$Percentage=8.889\times 10^{-13}$%

Explanation:

From special theory of relativity the dynamic mass m is related with the rest mass $m_{0}$of the body as

$m=\frac{m_{0} }{\sqrt{1-\frac{v^{2} }{c^{2} } } }$

Here, c is the speed of light and v is the velocity of object.

Given mass of the golf ball is 120 g.

$m=\frac{120 }{\sqrt{1-\frac{(40)^{2} }{(3\times 10^{8} )^{2} } } }\\m=120(1-\frac{(40)^{2} }{(3\times 10^{8}) ^{2} })^{-\frac{1}{2} }$

Now applying the binomial theorem and solve the above equation.

$m=(1+\frac{1}{2}(\frac{40}{3\times 10^{8} }) ^{2} )\\m=120(1+8.889\times 10^{-15})$

Therefore, increase in mass is,

$\Delta m=120\times 8.889\times 10^{-15} \\\Delta m=10.6668\times 10^{-13} g$

Now percentage of increase in mass with rest mass is,

$Percentage=\frac{10.6668\times 10^{-13} g}{120g} \times 100\\Percentage=8.889\times 10^{-13}$

Therefore, the percentage of increase in mass with rest mass is $Percentage=8.889\times 10^{-13}$.