If the dimensions of a physical quantity are $ML^2T^{-2}$, what could it represent?

The equation of a wave is given by $Y; = ;A\sin \omega \left( {\begin{array}{*{20}{c}}

{\frac{x}{\upsilon } - k}\

;

\end{array}} \right)$where$\omega $ is the angular velocity and υ is the linear velocity. The dimension of k is

Which of the following is dimensionally correct

Given, Force $= \frac{\alpha }{{{\rm{density}} + {\rm{\;}}{{\rm{\beta }}^3}}}$ What are the dimensions of ${\rm{\alpha }},{\rm{\beta }}?$

If F denotes force and t time, then in equation $F = a{t^{ - 1}} + \;b{t^2},$, the dimensions of a and b respectively are

The speed of sound in a medium depends on the modulus of elasticity $E$ and density $\rho$ of the medium. Using dimensional analysis, determine the relationship between these quantities.

If $S = \frac{1}{3}f{t^3},f$ has the dimensions of

The frequency of vibration of string is given by $v = \frac{P}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here p is number of segments in the string and $l$ is the length. The dimensional formula for m will be

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

The speed of light (c), gravitational constant (G) and Planck’s constant (h) are taken as the fundamental units in a system. The dimension of time in this new system should be

If the time period (T) of a simple pendulum depends on its length (L) and acceleration due to gravity (g), using dimensional analysis, find the relationship between T, L, and g.