Question

The velocity V is a particle at time t is given by
v=at+b/t+c

where a,b,c are constant.Calculate the dimension of of a,b,c.

Answer 1

Answer:

Explanation:

v = at + b/t + c

ok. here we know that the dimension of time t is [T] and that of velocity v is [LT⁻¹]

PRINCIPLE OF HOMOGENICITY STATES THAT THE DIMENSIONS IN THE LHS MUST BE EQUAL TO RHS ONLY THEN THE EQUATION IS CONSISTENT.

so our  DIMENSIONS IN THE LHS MUST BE EQUAL TO RHS.

[LT⁻¹] = a[T] + b/ [T] + c

so each and every term must be equal to  [LT⁻¹]

our first term, a[T] =  [LT⁻¹]

a =  [LT⁻¹] / [T]

∴ a = [LT⁻²]

second term , b/ [T] =  [LT⁻¹]

b = [LT⁻¹] [T]

∴ b = [L]

third term , dimension of c =  [LT⁻¹]

∴ c =  [LT⁻¹]

HENCE THE SOLUTION