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 .

Ten particles are moving at the speed of of 2,3,4,5,5,5,6,6,7 and 9 an

1.	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 .
Answer» Solution :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.