+1 vote
in Physical World and Measurement by (77.7k points)
closed by

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

(a) [L],[LT] and [LT-2]

(b) [LT-2], [L] and [T]

(c) [L2], [T] and [LT-2]

(d) [LT-2], [LT] and [L]

2 Answers

+1 vote
by (27.1k points)
selected by
Best answer

Answer: (b) [LT-2], [L] and [T]

According to the principle of dimensional homogeneity

Dimension of v = dimension of at = dimension of \(\frac{b}{t+c}\)

Dimension of a =\(\frac{\mathrm{[v]}}{[t]}=\frac{LT_2}{T}=[LT^{-2}]\)

Dimension of b =[v][t]=[LT-1T]=[L]

Dimension of c = [t]=[T]

+3 votes
by (75.7k points)

Correct Option  (b) [LT-2], [L] and [T]


v = at+ b/t+c

As c is added to t,

:. [c] = [T]

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.