If time t , velocity v , and angular momentum l are taken as the fundamental units. Then the dimension of…

If time t, velocity v, and angular momentum l are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is:
  1. t-1v1l-2
  2. t1v2l-1
  3. t-2v-1l1
  4. t-1v-2l1

Solution

m∝tavbℓc

m∝[T]aLT-1bML2 T-1c

M1 L0 T0=McLb+2cTa-b-c

Comparing powers, 

c=1, b=-2, a=-1

m∝t-1v-2ℓ1

Asked in: JEE Main 2021 (20 Jul Shift 2)

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