Velocity v and acceleration a in two systems of units 1 and 2 are related as v_2=nm^2v_1 and a_2=a_1mn respectively. Here m and n are constants. The relations for distance and time in two systems respectively are

Correct answer: (A) n^3 m^3 L_1=L_2 and n^2 m T_1=T_2. Distance is stated as [L]=(v^2)/([a]) ⇒v2^2a_2=(nm2v1^2a1mn^2=n^3m^3v1^2a_1Or, we have L_2=n^3m^3L_1Similarly, time T=v)/a ⇒v_2/a_2=(nm^2v_1)/a_1mn=n^2mv_1/a_1 So, T_2=n^2mT_1

Q61 / 90 · JEE Main 2022 (28 Jun Shift 2) · Physics

Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{m n}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are

Correct answer
A
$\frac{n^{3}}{m^{3}} L_{1} = L_{2}$ and $\frac{n^{2}}{m} T_{1} = T_{2}$
B
$L_{1} = \frac{n^{4}}{m^{2}} L_{2}$ and $T_{1} = \frac{n^{2}}{m} T_{2}$
C
$L_{1} = \frac{n^{2}}{m} L_{2}$ and $T_{1} = \frac{n^{4}}{m^{2}} T_{2}$
D
$\frac{n^{2}}{m} L_{1} = L_{2}$ and $\frac{n^{4}}{m^{2}} T_{1} = T_{2}$

Solution

Distance is stated as $[L] = \frac{[v^{2}]}{[a]}$

$\Rightarrow \frac{{[v_{2}]}^{2}}{[a_{2}]} = \frac{[{\frac{n}{m^{2}} v_{1}|}^{2}}{{[\frac{a_{1}}{m n}]}^{2}}$ $= \frac{n^{3}}{m^{3}} \frac{{[v_{1}]}^{2}}{[a_{1}]}$

Or, we have $[L_{2}] = \frac{n^{3}}{m^{3}} [L_{1}]$

Similarly, time $[T] = \frac{[v]}{[a]}$

$\Rightarrow \frac{[v_{2}]}{[a_{2}]} = \frac{[\frac{n}{m^{2}} v_{1}]}{[\frac{a_{1}}{m n}]} = \frac{n^{2}}{m} \frac{[v_{1}]}{[a_{1}]}$

So, $T_{2} = \frac{n^{2}}{m} T_{1}$

Hence, the correct answer is option: 'A'.

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

Solution

Relevant Questions

Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{m n}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are