The potential energy of a particle varies with distance $x$ from a fixed origin as $U=\frac{A \sqrt{x}}{x^2+B}$, where $A$ and $B$ are dimensional constants then dimensional formula for $A B$ is

  • A

    $\left[ ML ^{11/2} T ^{-2}\right]$

  • B

    $\left[ ML ^{7 / 2} T ^{-2}\right]$

  • C

    $\left[M^2 L^{9 / 2} T^{-2}\right]$

  • D

    $\left[ ML ^{13 / 2} T ^{-3}\right]$

Similar Questions

The equation of the stationary wave is
$y = 2A\,\,\sin \,\left( {\frac{{2\pi ct}}{\lambda }} \right)\,\cos \,\,\,\left( {\frac{{2\pi x}}{\lambda }} \right)$
Which statement is not true?

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$ : Time period of oscillation of a liquid drop depends on surface tension $(S)$, if density of the liquid is $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.
Reason $(R)$: Using dimensional analysis we get $R.H.S.$ having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

  • [JEE MAIN 2022]

Density of wood is $0.5 \;gm / cc$ in the $CGS$ system of units. The corresponding value in $MKS$ units is.?

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Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.