Question

11)Ten particles are moving at the speed of 2, 3, 4, 5, 5, 5, 6, 6, 7 and 9 m s-¹.Find the rms speed.... *

1 point

5.53 ms-¹

6.53 ms-¹

5 ms-¹

6 ms-¹

​

Answer 1

Given :-

• Ten particles are moving at the speed of 2, 3, 4, 5, 5, 5, 6, 6, 7 and 9 ms⁻¹

To Find :-

• The RMS Speed

Solution :-

RMS Speed is defined as the value of root over sum of the squares of speeds divided by the number of speeds.

So , RMS speed of the given partickes is ;

$\\ : \implies \sf \: v_{rms} = \sqrt{ \frac{ {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2} + {(5)}^{2} + {(5)}^{2} + {(6)}^{2} + {(6)}^{2} + {(7)}^{2} + {(9)}^{2} }{10} }$

$\\ : \implies \sf \: v_{rms} = \sqrt{ \frac{4 + 9 + 16 + 25 + 25 + 25 + 36 + 36 + 49 + 81}{10} }$

$\\ : \implies \sf \: v_{rms} = \sqrt{ \frac{306}{10} }$

$\\ : \implies \sf \: v_{rms} = \sqrt{30.6}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{v_{rms} = 5.53 \: m {s}^{ - 1} }}}}} \: \bigstar$

Hence ,

• The RMS speed of given particles is 5.53 m/s

Answer 2

Question :-

Ten particals are moving at the speed of 2, 3, 4, 5, 5, 5, 6, 6, 7 and 9 m/s. Find the RMS speed ....

1. 5.53 m/s
2. 6.53 m/s
3. 5 m/s
4. 6 m/s

Given :-

The speed of particals is -

• 2, 3, 4, 5, 5, 5, 6, 6, 7 and 9 m/s

Solution :-

We know that,

• $\sf \: v_{rms} = \sqrt{ \frac{sum \: of \: squares \: of \: speed}{numbers \: of \: particals} }$

So,

$\sf \star \: v_{rms} = \sqrt{ \frac{ {(2)}^{2} + {(3)}^{2} + {(4)}^{2} + {(5)}^{2} + {(5)}^{2} + {(5)}^{2} + {(6)}^{2} + {(6)}^{2} + {(7)}^{2} + {(9)}^{2} }{10} } \\ \\ \mapsto \sf v_{rms} = \sqrt{ \frac{4 + 9 + 16 + 25 + 25 + 25 + 36 + 36 +49 + 81 }{10 } } \\ \\ \mapsto \sf \: v_{rms} = \sqrt{ \frac{306}{10} } \\ \\ \mapsto \sf \: v_{rms} = \sqrt{30.6} \\ \\ \mapsto \boxed{\sf \: v_{rms} = 5.53 \: {ms}^{ - 1} }$

Hence, the rms speed is 5.53 m/s. So the option 1 is correct.

Explanation :-

RMS speed is Root means square speed. RMS speed is the measure of speed of particals in a gas defined as the square root of the average velocity - squared of a molecules in a gas.

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