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Question

The velocity of a particle depends upon time according to the relation v=αt+β/t+y. The dimensions of α,β and y will be :

A
LT2,L,LT1
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B
L,LT1,LT2
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C
LT1,L,LT2
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D
LT1,L,T1L
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Solution

The correct option is B LT2,L,LT1
Since the unit of velocity is meter per second its dimensions are
[LT1]
In order to equate the given equation the dimensions on either sides should be equal to [LT1]
Given equation in dimensional form is
[LT1]=α[T1]+β[T1]+y
To obtain required dimensions we write equation as
[LT1]=[LT2][T1]+[L][T1]+[LT1]
Comparing both equations we get
α=[LT2],β=[L],y=[LT1]

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