The velocity of a freely falling body changes as ${g^p}{h^q}$ where g is acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are

  • A

    $1,\frac{1}{2}$

  • B

    $\frac{1}{2},\frac{1}{2}$

  • C

    $\frac{1}{2},\,1$

  • D

    $1,\,1$

Similar Questions

Match List $I$ with List $II$

List $I$ List $II$
$A$ Spring constant $I$ $(T ^{-1})$
$B$ Angular speed $II$ $(MT ^{-2})$
$C$ Angular momentum $III$ $(ML ^2)$
$D$ Moment of Inertia $IV$ $(ML ^2 T ^{-1})$

Choose the correct answer from the options given below

  • [JEE MAIN 2023]

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

The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........

A calorie is a unit of heat or energy and it equals about $4.2\; J$ where $1 \;J =1\; kg \,m ^{2} \,s ^{-2}$ Suppose we employ a system of units in which the unit of mass equals $\alpha\; kg$, the unit of length equals $\beta\; m$, the unit of time is $\gamma$ $s$. Show that a calorie has a magnitude $4.2 \;\alpha^{-1} \beta^{-2} \gamma^{2}$ in terms of the new units.

Which of the following is not a dimensionless quantity?

  • [JEE MAIN 2021]