Physical World Units and Measurements - Result Question 18

18. The velocity v of a particle at time t is given by v=at+bt+c, where a,b and c are constant. The dimensions of a,b and c are respectively

[2006]

(a) [L2,T. and .LT2]

(c) [L,LT. and .T2]

(b) [LT2,LT. and .L]

(d) [LT2,L. and .T]

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Answer:

Correct Answer: 18. (d)

Solution:

  1. (d) Dimension of at= dimension of velocity

a.t =[LT1][a=LT2]

Dimension of c= dimension of t

(two physical quantity of same dimension can only be added)

So, dimension of c=[T]

Dimension of bt+c= Dimension of velocity

bT+T=[LT1][LT1][bT1]=[LT1]

b=[L]

So, answer is [LT2], [L] and [T]

A dimensionally correct equation may or may not be physically correct. In a dimensionally correct equation, the dimensions of each term on both sides of an equation must be the same.



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