Question

A study of automobile speeds on a highway yielded the following data for a 1 hour period-

Speed in km/hr Number of cars (n)

(i) 40 10

(ii) 45 8

(iii) 50 15

(iv) 55 10

(v) 60 12

Which of the following is/are correct-

• A. The most probable speed of the automobile is 50 km/hr
• B. The root mean square speed 51 km/hr
• C. The value of $\frac{u_{avg}}{u_{rms}}$ is not equal to $\sqrt{\frac{8}{3\pi}}$
• D. All of the above are correct

Answer 1

Answer: (D)

All of the above are correct

Answer 2

U_rms=

$\sqrt{\frac{10 \times (40)^{2} + 8 \times (45)^{2} + 15 \times (50)^{2} + 10 \times (55)^{2} + 12 \times (60)^{2}}{55}}$

U_rms = $\sqrt{\frac{16000 + 16,200 + 37,500 + 30,250 + 43,200}{55}}$

U_rms = 51.01 kms/hr.

U_avg = $\frac{10 \times 40 + 8 \times 45 + 15 \times 50 + 10 \times 55 + 12 \times 60}{55}$

U_avg = 50.54 kms/hr.

\ $\frac{U_{avg}}{U_{rms}}$ ¹ $\sqrt{\frac{8}{3\pi}}$