Velocity v and acceleration a in two systems of units 1 and 2 are related as v 2 = n m 2 v 1 and a 2 = a 1 m…

Velocity v and acceleration a in two systems of units 1 and 2 are related as v2=nm2v1 and a2=a1mn respectively. Here m and n are constants. The relations for distance and time in two systems respectively are
  1. n3 m3 L1=L2 and n2 m T1=T2
  2. L1=n4 m2 L2 and T1=n2 m T2
  3. L1=n2mL2 and T1=n4m2T2
  4. n2 m L1=L2 and n4 m2 T1=T2

Solution

Distance is stated as [L]=v2[a]

 ⇒v22a2=nm2v12a1mn2=n3m3v12a1

Or, we have L2=n3m3L1

Similarly, time T=va

⇒v2a2=nm2v1a1mn=n2mv1a1

So, T2=n2mT1

Asked in: JEE Main 2022 (28 Jun Shift 2)

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