The conversion of $1 \;MW$ power in a new system having basic units of mass,length,and time as $10 \;kg$,$1 \;dm$,and $1 \;minute$ respectively is:

$A$ gas bubble from an explosion under water oscillates with a period proportional to $P^a d^b E^c$,where $P$ is the static pressure,$d$ is the density of water,and $E$ is the energy of the explosion. Then $a, b,$ and $c$ are:

$A$ small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time,the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on $(i)$ the mass of the ball $m$,$(ii)$ $\eta$,$(iii)$ $r$,and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct?

If $y$ represents pressure and $x$ represents velocity gradient,then the dimensions of $\frac{d^2 y}{d x^2}$ are

If $E$,$L$,$m$ and $G$ denote the quantities as energy,angular momentum,mass and constant of gravitation respectively,then the dimensions of $P$ in the formula $P = EL^2 m^{-5} G^{-2}$ are

Write and explain the principle of homogeneity. Check the dimensional consistency of the given equation: $x = x_{0} + v_{0}t + \frac{1}{2}at^{2}$.