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
$1,\frac{1}{2}$
$\frac{1}{2},\frac{1}{2}$
$\frac{1}{2},\,1$
$1,\,1$
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
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 ..........
Which of the following is not a dimensionless quantity?