Question

the distance covered by partial in time t is x= a t + b t3. the dimension of a and b are
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Answer 1

Answer:

Correct question:

Distance covered by a particle in time 't' is given as:

x = at + bt³. Find the dimensions of 'a' and 'b'.

Concept: For two things to be added, they must be of same dimensions.

For example, if we want to add 5 kg and 5 m, it is not possible since both have different units which means different dimensions.

Hence if you want to add distances, you should only have the dimensions of distance.

According to the given question, 'x' represents distance. Hence the RHS should also have the net dimension to be same as LHS.

Dimension of x = [ M⁰LT⁰ ]

Therefore, Dimension of at should also be  [ M⁰LT⁰ ].

Dimension of at = [ x ] [ M⁰L⁰T¹ ]

Hence dimension of 'a' should be = [ M⁰L¹T⁻¹]

So that, when dimensions of 'a' and 't' are multiplied you get final dimension to be  [ M⁰LT⁰ ].

For bt³ dimensions are = [ x ] [ M⁰L⁰T³ ]

Hence for b, the dimensions are = [ M⁰L¹T⁻³]

So that, when dimensions of 'b' and 't³' are multiplied you get final dimension to be  [ M⁰LT⁰ ].