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A flask has 10 gas particles, out of whi...

A flask has 10 gas particles, out of which four particles are moving at 7 `ms^(-1)` and the remaining are moving at the same speed of `'X' ms^(-1)` . If the r.m.s. of the gas is `5ms^(-1)` , what is the value of X ?

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The correct Answer is:
3
`v_(rms) (5 ms^(-1))`
`= sqrt((4 xx 7^(2) xx 6x^(2))/(4 + 6)) = sqrt((196 + 6 x^(2))/(10))`
Squaring both sides
`25 = (196 + 6x^(2))/(10) " or " 250 = 196 + 6x^(2)`
`:. 6x^(2) = 54 " or " x^(2) = 9 " or " x = 3`
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