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JEE MAINS 2024
31.01.24 S1
Question
A force is represented by $F=a x^2+b t^{1 / 2}$ Where $\mathrm{x}=$ distance and $\mathrm{t}=$ time. The dimensions of $\mathrm{b}^2 / \mathrm{a}$ are i
Select the correct option:
A
$\left[\mathrm{ML}^3 \mathrm{~T}^{-3}\right]$
B
$\left[\mathrm{MLT}^{-2}\right]$
C
$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$
D
$\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. $$ \begin{aligned} & F=a x^2+b t^{1 / 2} \\ & {[\mathrm{a}]=\frac{[\mathrm{F}]}{\left[\mathrm{x}^2\right]}=\left[\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]} \\ & {[\mathrm{b}]=\frac{[\mathrm{F}]}{\left[\mathrm{t}^{1 / 2}\right]}=\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-5 / 2}\right]} \\ & {\left[\frac{b^2}{a}\right]=\frac{\left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-5}\right]}{\left[\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]}=\left[\mathrm{M}^1 \mathrm{~L}^3 \mathrm{~T}^{-3}\right]} \end{aligned} $$
Question Tags
JEE Main
Physics
Medium
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