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Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as v₂=n/(m²)v₁ and a₂=(a₁)/(mn) respectively. Here m and n are constants. The relations for distance and time in two systems respectively are

Asked in JEE Main 28th June 2nd Shift 2022 · Expressing a quantity in new base units

• (1) (n³)/(m³)L₁=L₂ and (n²)/mT₁=T₂
• (2) L₁=(n⁴)/(m²)L₂ and T₁=(n²)/mT₂
• (3) l₁=(n²)/mL₂ and T₁=(n⁴)/(m²)T₂
• (4) (n²)/mL₁=L₂ and (n⁴)/(m²)T₁=T₂

Step-by-step solution

Why the other options are wrong

• (2) comes from inverts which system carries the factor
• (3) comes from swaps the length and time factors
• (4) comes from uses the time factor for the length and the length factor for the time

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