Ten particles are moving at the speed of of 2,3,4,5,5,5,6,6,7 and 9 and `ms^(-1)`. Calculate rms speed , average speed and most probable speed .

Explanation

The average speed `bar nu=(2+3+4+5+5+5+6+6+7+9)/10=5.2"ms"^(-1)`
To find the rms speed, first calculate the mean square speed `barv^(2)`
`bar(nu^(2))=(2^(2)+3^(2)+4^(2)+5^(2)+5^(2)+5^(2)+6^(2)+6^(2)+7^(2)+9^(2))/10=30.6 m^(2)s^(-2)`
The rms speed `nu_(rms)=sqrt(nu^bar(2))=sqrt(30.6)=5.53ms^(-1)`
The most probable speed is `5ms^(-1)` because three of the pearticles have that speed.