Velocity Time considered |Units and MeasurementsJEEMain2023

JEE MAIN 2023

11-4-2023

Question

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:

Select the correct option:

$\mathrm{FV}^{-2} \mathrm{~T}^2$

$F V^{-4} T^2$

$\mathrm{FV}^4 \mathrm{~T}^{-6}$

$\mathrm{F}^2 \mathrm{~V}^{-2} \mathrm{~T}^6$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Sol. $$ \begin{aligned} & {\left[\mathrm{ML}^{-3}\right]=\left[\mathrm{MLT}^{-2}\right]^{\mathrm{a}}\left[\mathrm{LT}^{-1}\right]^{\mathrm{b}}[\mathrm{~T}]^{\mathrm{c}}} \\ & \left.=\left[\mathrm{M}^{\mathrm{a}} L^{\mathrm{a}+\mathrm{b}} \mathrm{~T}^{-2 \mathrm{a}-\mathrm{b}^{+} \mathrm{c}}\right]\right] \\ & \mathrm{a}=1 \\ & \mathrm{a}+\mathrm{b}=-3 \\ & \Rightarrow \mathrm{~b}=-4 \\ & \text { Also, }-2 \mathrm{a}-\mathrm{b}+\mathrm{c}=0 \\ & \mathrm{c}=-2 \end{aligned} $$

Question Tags

JEE Main

Chemistry

Hard

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