The kinetic energy possessed by a body of mas | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The classical expression for kinetic energy,$K = \frac{1}{2}mv^2$,is derived from Newtonian mechanics.According to Einstein's theory of special re

Vedclass · Accepted Answer

The body moves with velocities negligible compared to the speed of light

Vedclass · Answer

(B) The classical expression for kinetic energy,$K = \frac{1}{2}mv^2$,is derived from Newtonian mechanics.According to Einstein's theory of special relativity,the total energy of a body is given by $E = \gamma mc^2$,where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$.The kinetic energy is the difference between the total energy and the rest energy: $K = E - mc^2 = mc^2(\gamma - 1)$.Using the binomial expansion for $\gamma$ when $v \ll c$,we get $\gamma \approx 1 + \frac{1}{2}\frac{v^2}{c^2}$.Substituting this back,$K \approx mc^2(1 + \frac{1}{2}\frac{v^2}{c^2} - 1) = \frac{1}{2}mv^2$.Thus,the classical formula is valid only when the velocity of the body is negligible compared to the speed of light.

The kinetic energy possessed by a body of mass $m$ moving with a velocity $v$ is equal to $\frac{1}{2}mv^2$,provided

Similar Questions

When kinetic energy of a body becomes $36$ times of its original value,the percentage increase in the momentum of the body will be : (in $\%$)

$A$ particle of mass $m$ at rest is acted upon by a force $F$ for a time $t$. Its kinetic energy after an interval $t$ is

If the increase in the kinetic energy of a body is $22\%$,then the increase in the momentum will be ........... $\%$

$A$ body of mass $m$ moving with velocity $v$ has kinetic energy equal to $\frac{1}{2} mv^2$. This statement is valid when:

$A$ particle is released freely from a height $H$. At a certain height,its kinetic energy is two times its potential energy. Then,the height and the speed of the particle at that instant are respectively ($g=$ acceleration due to gravity).

Vedclass Test Series

Exam Paper Generator

Online Exam Module