Q. The velocity v of a particle at time t is given by v = at + b/(t + c), where a, b and c are constants. The dimensions of a, b and c are respectively :
A) [LT⁻²], [L] and [T]
B) [L], [T] and [LT²]
C) [L²T²], [LT] and [L]
D) [L], [LT] and [T²]
Explanation
[Solution from source] Every term must have the dimensions of velocity [LT⁻¹]. From at, a = [LT⁻²]. In b/(t + c), c is added to time so c = [T]; then b/[T] = [LT⁻¹] gives b = [L]. The other choices fail the rule that only like quantities can be added. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.