Question

Fifteen identical particles have various speeds. One has a speed of 3.00 m/s, two have a speed of 4.00 m/s, three have a speed of 6.00 m/s, four have a speed of 6.00 m/s, three have a speed of 8.00 m/s and two have a speed of 10.0 m/s. Find (a) the average speed, (b) the rms speed, and (c) the most probable speed of these particles.

Question 17 options:

a	(a) 6.17 m/s; (b) 8.76 m/s; (c) 6.00 m/s
b	(a) 6.47 m/s; (b) 6.76 m/s; (c) 7.00 m/s
c	(a) 6.47 m/s; (b) 6.76 m/s; (c) 10.0 m/s
d	(a) 6.47 m/s; (b) 6.76 m/s; (c) 6.00 m/s
e	(a) 6.80 m/s; (b) 7.41 m/s; (c) 7.00 m/s

Answer 1

n ） -> Given 15 identical partides have various speeds. 3,4,4,6,6,6,6,6,6,6,8,8,8, 10, 10 m/s a) The average speed N=15 (Totel number Vaug = &nivi of particles N of Mz (number of particles having speed 14 ) = 1 0,=3 m/s na (number of particles having speed U2) = 8 U2=4 m/s M3 (number particles having speed U3) = 7 Ug = 6 m/s mu (number of particles having speed vu)= 3 Vu=8 m/s ms (number of particles having speed Us)= . Us=lom/s niet n2 th3 Uz they + ng us o = Vaug N 1x3+ &X4+7X6+3X8+ 2X10_97 ū is 15 Vaug 6.46 m/s b) Root-mean- n-square uare speed Vorms = Jua ū° = mi via nie + n20 + 120 st huvitngus N N

2 GI مع 1X (3)+2x(4)+7X16)+ 3x (8)2+ 2X (10)? = IS 9+32+252 +192 +200 685 15 15 ūd = 45.66m/s =) Usims - J45.66 =) Urms = 6.75 m/s C) As we can see from data that 7 particles have a speed of 6 m/s, three particles have a speed of 8 m/s, two particles have a speed of 20m/s, two particles have a speed of and one particle have a speed of 3m/s. There fore the most probable speed of these particles is : Ump = 6 m/s 4 m/s Results, Vaug = 6.46m/s Vrms = 6.75 ms lehus-@ Omp = 6 m/s