Question

A force f is given by f=at +bt2 where t is time . The dimentions of a and b are

Answer 1

[Force]= [MLT-²]

Now, by principal of homogeneity we know that the physical quantities have equal dimensions on the RHS and LHS side and only like quantities can be added or subtracted.

So,

[MLT-²]=[at]=[bt²]

Now,

MLT-² = aT

a = [MLT-²]/[T]

a = [MLT-³]

Again,

[MLT-²] = [bT²]

b = [MLT-²][/T²]

b = [MLT-⁴]

Cheers!

Answer 2

Answer:

a=MLT-3 b=MLT-4

dimension of a is MLT-3

and b has MLT-4