Question

Marks: +3
A flask has 10 gas particles out of which four particles are moving at 7m/s and the remaining are moving at
the same speed of 'X'm/s. If the rms of the gas is 5m/s, what is the value of X?​

Answer 1

Given:

Total no of particles, n = 10

RMS speed = 5 m/s

Speed of 4 particles, v1 = 7 m/s

Speed of remaining 6 particles, v2 = X m/s

To Find:

The value of X.

Calculation:

- RMS value is given as:

RMS = √(∑V²/∑n)

⇒ RMS² = (4 v1² + 6 v2²)/10

⇒ 5² = 4 (7)² + 6 v2²/10

⇒ v2² = {(25 × 10)-(4 × 49)}/6

⇒ v2² = (250-196)/6

⇒ v2² = 54/6

⇒ v2 = √9

⇒ v2 = 3 m/s = X

- So, the value of X is 3 m/s.