NEET Physics Question - Gravitation

A force F is given by F = at + bt², where t is time. The dimensions of a and b are

[M L T–³] and [M L T–4]

[M L T–4] and [M L T–³]

[M L T–¹] and [M L T–²]

[M L T–²] and [M L T0]

The force \( F = at + bt^2 \) has dimensions of force \([M L T^{-2}]\).

For \( at \), the dimensions of \( a \) must be:

\[
[M L T^{-2}] = [a][T]
\]

Thus, the dimensions of \( a \) are:

\[
a = [M L T^{-3}]
\]

For \( bt^2 \), the dimensions of \( b \) must be:

\[
[M L T^{-2}] = [b][T^2]
\]

Thus, the dimensions of \( b \) are:

\[
b = [M L T^{-4}]
\]

So, the dimensions are:
- \( a = [M L T^{-3}] \)
- \( b = [M L T^{-4}] \)

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