To keep on object moving in a circle at constant speed requ…

Physics Units, Dimensions and Measurement Dimensions MCQ (Single Correct)

To keep on object moving in a circle at constant speed requires a force F α m a v b r c . According to dimensional analysis the a, b, c are -

a = 1, b = 2, c = –1

a = 1, b = 2, c = 1

a = 0, b = 2, c = – 1

a = 1, b = 2, c = 0

Text Solution

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The correct answer is:

F ∝ m a v b r c

i.e. [F] = [m] a [v] b [r] c or[M

1 L 1 T -2 ] = [M a ] [L 1 T -1 ] b [L] C or[M

1 L 1 T -2 ] = [M a L b+c T -b ]

comparing LHS and RHS

a = 1, b + c = 1 & –b = –2

⇒ a = 1, b = 2, c = –1

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