Two particles of the same mass are moving in | vedclass

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

Question

As the particles moving in circular orbits, So

$\frac{{m{v^2}}}{r} = \frac{{16}}{r} + {r^3}$

Kinetic energy, $K{E_0} = \frac{1}{2}m{v^2} =

Vedclass · Accepted Answer

$6 	imes {10^{-2}}$

Vedclass · Answer

As the particles moving in circular orbits, So

$\frac{{m{v^2}}}{r} = \frac{{16}}{r} + {r^3}$

Kinetic energy, $K{E_0} = \frac{1}{2}m{v^2} = \frac{1}{2}\left[ {16 + {r^4}} ight]$

For fist particle, $r = 1,$ ${K_1} = \frac{1}{2}\left( {16 + 1} ight)$

Similarly, for second particle, $r = 4,$

${K_2} = \frac{1}{2}\left( {16 + 256} ight)$

$	herefore \,\frac{{{K_1}}}{{{K_2}}} = \frac{{\frac{{16 + 1}}{2}}}{{\frac{{16 + 256}}{2}}} = \frac{{17}}{{272}} \simeq 6 	imes {10^{ - 2}}$

Similar Questions

The slope of kinetic energy displacement curve of a particle in motion is

A wooden block of mass $M$ is suspended by a cord and is at rest. A bullet of mass $m,$ moving with a velocity $v$ passes through the block and comes out with a velocity $v/2$ in the same direction. If there is no loss in kinetic energy, then upto what height the block will rise

A bomb of mass $9\,kg$ explodes into $2$ pieces of mass $3\,kg$ and $6\,kg.$ The velocity of mass $3\,kg$ is $1.6\, m/s$, the K.E. of mass $6\,kg$ is ............ $J$

A block moving horizontally on a smooth surface with a speed of $40\, {m} / {s}$ splits into two parts with masses in the ratio of $1: 2$. If the smaller part moves at $60\, {m} / {s}$ in the same direction, then the fractional change in kinetic energy is :-