JEE Main 2022 · 28 Jun · Shift 2 · Physics Q31

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PhysicsSingle correct+4 / -1Question 31 of 90

Velocity ( $v$ ) and acceleration ( $a$ ) in two systems of units 1 and 2 are related as $v_2=\dfrac n{m^2}v_1$ and $a_2=\dfrac{a_1}{mn}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are :

\dfrac{n^3}{m^3}L_1=L_2

and

\dfrac{n^2}mT_1=T_2

L_1=\dfrac{n^4}{m^2}L_2

and

T_1=\dfrac{n^2}mT_2

L_1=\dfrac{n^2}mL_2

and

T_1=\dfrac{n^4}{m^2}T_2

\dfrac{n^2}mL_1=L_2

and

\dfrac{n^4}{m^2}T_1=T_2

Answer and worked solution

Official answer: A

Time $=\frac va$ : $T_2=T_1\cdot\frac n{m^2}\cdot mn=\frac{n^2}mT_1$ .

Length $=\frac{v^2}a$ : $L_2=L_1\cdot\frac{n^2}{m^4}\cdot mn=\frac{n^3}{m^3}L_1$ .

(A)

Topics:SI units and systems of units Dimensional analysis

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JEE Main 2022 · 28 Jun · Shift 2, Physics question 31