Concepts Of Physics MCQ Edition [Volume 1]PhysicsIntroduction to Physics
Assume a quantity x can be dimensionally expressed in terms of M , L , and T , such that [x] = M^a L^b T^c . The quantity mass
Options
- Amay be expressed in terms of L , T , and x if a 0
- Bcan never be dimensionally expressed in terms of L , T , and x
- Ccan always be dimensionally expressed in terms of L , T , and x
- Dmay be expressed in terms of L , T , and x if a = 0
Correct answer
A. may be expressed in terms of L , T , and x if a 0
Step-by-step solution
Given [x] = M^a L^b T^c Rearranging the terms to express M in terms of x , L , and T : M^a = [x] L^ -b T^ -c M = [x]^ 1/a L^ -b/a T^ -c/a For this relation to be valid, the exponent 1/a must be defined, which requires a 0 . Therefore, mass may be expressed in terms of L , T , and x if a 0 .