Question

Nine particles have speeds of 5.00, 8.00, 12.0, 12.0, 12.0, 14.0, 14.0, 17.0, and 20.0 m/s. What is the rms speed?
a. 9.35 m/s b . 13.3 m/s c. 12.3 m/s d. 14.7 m/s​

Answer 1

$\mathfrak{\huge{\underline{Answer:}}}$

•GIVEN:

Speed of nine different particles as 5,8,12,12,12,14,14,17,20

•TO FIND:

RMS speed ${V}_{rms}$ speed of the given data.

FORMULA;

V_{rms}=$\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}}{n} }$

Where n is the number of particles given

$V_{rms}$=$\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}+v_{5}^{2}+v_{6}^{2}+v_{7}^{2}+v_{8}^{2}+v_{9}^{2}}{9} }$

$V_{rms}$=$\sqrt{\frac{5^{2}+8^{2}+12^{2}+12^{2}+12^{2}+14^{2}+14^{2}+17^{2}+20^{2}}{9} }$

$V_{rms}$=$\sqrt{178}$

$V_{rms}$=13.4

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\small{\underline{\blue{\sf{Given :}}}}$

• Speeds are : 5,8,12,12,12,14,14,17,20 m/s

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$\small{\underline{\green{\sf{Solution :}}}}$

We have formula for Root Mean Speed :

$\large \star {\boxed{\sf{v_{rm} \: = \: \sqrt{\dfrac{v_1 ^2 \: + \: v_2 ^2 \: + \: ........ \: + \: v_n ^2}{n}}}}} \\ \\ \footnotesize \implies {\sf{v_{rm} \: = \: \sqrt{\dfrac{(5)^2 \: + \: (8)^2 \: + \: (12)^2 \: + \: (12)^2 \: + \: (12)^2 \: + \: (14)^2 \: + \: (14)^2 \: + \: (17)^2 \: + \: (20)^2}{9}}}} \\ \\ \footnotesize \implies {\sf{v_{rm} \: = \: \sqrt{\dfrac{25 \: + \: 64 \: + \: + \: 144 \: + \: 144 \: + \: 144 \: + \: 196 \: + \: 196 \: + \: 289 \: + \: 400}{9}}}} \\ \\ \implies {\sf{v_{rm} \: = \: \sqrt{\dfrac{1602}{9}}}} \\ \\ \implies {\sf{v_{rm} \: = \: \sqrt{178}}} \\ \\ \implies {\sf{v_{rm} \: = \: 13.4}} \\ \\ {\boxed{\sf{\therefore \: Vrm \: Speed \: = \: 13.4 \: ms^{-1}}}}$