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JEE Main202228 Jun 2022Evening ShiftPhysicsMotion in One DimensionActual

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 n respectively. Here m and n are constants. The relations for distance and time in two systems respectively are

Options

  1. An 3   m 3   L 1 = L 2 and n 2   m   T 1 = T 2
  2. BL 1 = n 4   m 2   L 2 and T 1 = n 2   m   T 2
  3. CL 1 = n 2 m L 2 and T 1 = n 4 m 2 T 2
  4. Dn 2   m   L 1 = L 2 and n 4   m 2   T 1 = T 2

Correct answer

A. n 3   m 3   L 1 = L 2 and n 2   m   T 1 = T 2

Step-by-step solution

Distance is stated as [ L ] = v 2 [ a ] ⇒ v 2 2 a 2 = n m 2 v 1 2 a 1 m n 2 = n 3 m 3 v 1 2 a 1 Or, we have L 2 = n 3 m 3 L 1 Similarly, time T = v a ⇒ v 2 a 2 = n m 2 v 1 a 1 m n = n 2 m v 1 a 1 So, T 2 = n 2 m T 1

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