Question

show that 1/2 gt2 has same dimension of distance

Answer 1

The dimension of 1/2 gt^2

= (LT^-2)(T)^2

=LT^-2T^2

=L

Since the dimension of distance = L

Therefore the dimesion is same

Answer 2

Answer:

Since g is acceleration due to gravity, then its dimensions are the same as that of acceleration. therefore,[g]= [LT^-2].

Now, dimension of 1/2[gt^2]=[L]

We can write constant as it is dimensionless.

[gt^2]=[L]

⇒ [g][t^2]=[L]

⇒ [g]=[L]/[t^2]

⇒ [g]=[L]/([T]^2)

⇒ [g]=[LT^-2]

[Writing conventions may differ.]

Hence, Dimension of g = M°LT^(-2) or L/T²