Physics And Measurement Question 97
Question: If $ P $ represents radiation pressure, $ c $ represents speed of light and $ Q $ represents radiation energy striking a unit area per second, then non-zero integers $ x,y $ and $ z $ such that $ P^{x}Q^{y}c^{z} $ is dimensionless, are
[AFMC 1991; CBSE PMT 1992; CPMT 1981, 92; MP PMT 1992]
Options:
A) $ x=1,y=1,z=-1 $
B) $ x=1,y=-1,z=1 $
C) $ x=-1,y=1,z=1 $
D) $ x=1,y=1,z=1 $
Show Answer
Answer:
Correct Answer: B
Solution:
By substituting the dimension of given quantities
$ {{[M{{L}^{-1}}{{T}^{-2}}]}^{x}}{{[M{{T}^{-3}}]}^{y}}{{[L{{T}^{-1}}]}^{z}}={{[MLT]}^{0}} $
By comparing the power of M, L, T in both sides $ x+y=0 $ …..(i)
$ -x+z=0 $ …..(ii)
$ -2x-3y-z=0 $ -(iii)
The only values of $ x,y,z $ satisfying (i), (ii) and (iii) corresponds to .
