JEE Advanced · PhysicsHard

$In a new system of units, the unit of mass is α kg, the unit of length is β m, and the unit of time is γ s . If the value of force in this new system is F^{'}, find the value of force in SI units.$

A. $F^{'} α β γ^{- 2}$
B. $F^{'} α β γ^{- 1}$
C. $F^{'} α β^{2} γ^{- 1}$
D. $F^{'} α β^{2} γ^{- 2}$

Show correct answer & step-by-step solution

Correct answer: A — $F^{'} α β γ^{- 2}$

Solution

$The dimensional formula for force is [M L T^{- 2}] .$
$Let n_{1} u_{1} = n_{2} u_{2}, where n_{1} is the value in SI and n_{2} = F^{'} is the value in the new system.$
$n_{1} (1 kg) (1 m) (1 s)^{- 2} = F^{'} (α kg) (β m) (γ s)^{- 2} .$
$n_{1} = F^{'} α β γ^{- 2} .$
$Hence the answer is (A).$

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