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Question

Which of the following is dimensionless?


A

v2rg

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B

v2gr

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C

v2gr

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D

v2rg

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Solution

The correct option is A

v2rg


Explanation for the correct option:

A: v2rg

  1. Given v is the speed,ris the radius, and g is the gravitational acceleration.
  2. Check it out by putting [v]=LT1,[r]=[L],[g]=LT2

v2rg=LT12L1L1T2=M0L0T0

Explanation for the incorrect option(s):

B: v2gr

v2rg=L1T12L1L2=L2

C: v2gr

v2gr=LT12LT2L=L2T4

D: v2rg

v2rg=LT12L1LT1=L4T3

Hence, option (A) is the correct answer.


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