Question

3.
A force F is given by F = at + bt?, where t is
time. The dimension of a and b are
(1) MLT-?] and [
MLT-4]
(2) ML T4] and [M LT-3]
(3) [ML T-'] and [
ML T-?]
(4) [ML T-?] and [
ML T]
ans and explain it.​

Answer 1

Answer:

The Question is Wrong with the wrong options.

Explanation:

Correction: A force F is given by F = at + bt², where t is time. The dimensions of 'a' and 'b' are:

Solution: Since the SI unit of force is kg.m/s²(or Newton), so

Dimension of force is [ MLT^-2].

According to the principle of homogeneity of dimensions, the dimensions of each and every term on either sides of a correct physical relations are same.

i.e. [F] = [at]

or, [F/t] = [a]

or, [a] = [MLT^-2]/[T] = [MLT^-3]

Again,

[F] = [bt²]

or, [F/t²] = [b]

or, [ MLT^-2]/[T^2] = [b]

or, [b] = [MLT^-4]

Hence, the dimensions of 'a' and 'b' are [MLT^-3] and [MLT-4] respectively .