Whether a given relation / formula is co...

Whether a given relation / formula is correct or not can be checked on the basis of the principle of homogeneity of dimensions. According to this principle, only that formula is correct, in which the dimensions of the various terms on one side of the relation are equal to the respective dimensions of these terms on the other side of the relation. With the help of the compreshension given above, choose the most appropriate alternative for each of the following questions :
The distance travelledl by a body in nth second is given by `S_(nth) = u + (a)/(2) (2n-1)` where u is initial velocity and a is acceleration. The dimensions of `S_(nth)` are

`LT^(-1)`

`LT^(-2)`

`L^(-1)T`

Verified by Experts

The correct Answer is:

(b)

`S_(nth)` = distance travelled by a body in one particular second `=(L)/(T) LT^(-1)`

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Whether a given relation / formula is correct or not can be checked on the basis of the principle of homogeneity of dimensions. According to this principle, only that formula is correct, in which the dimensions of the various terms on one side of the relation are equal to the respective dimensions of these terms on the other side of the relation. With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions : In the same equation, the dimensional formula of a is

`[M^(-1) L^0 T^2]`

`[ML^0 T^2]`

`[ML^(-1) T^(-2)]`

`[M^(-1) L^1 T^(-2)]`

`T^(2)=(4pi^(2)r^(3))/(GM)`

`T^(2)=4pi^(2)r^(2)`

`T^(2)=(4pi^(2)r^(3))/(G)`

`T=(4pi^(2)r^(3))/(G)`

`M^(2)L^(-2)T^(-2)`

`M^(0)L^(0)T^(0)`

`M^(1)L^(1)T^(-2)`

`M^(1)L^(1)T`