If time $(t)$,velocity $(u)$,and angular momentum $(I)$ are taken as the fundamental units,then the dimension of mass $(m)$ in terms of $(t)$,$(u)$,and $(I)$ is:

Consider a spongy block of mass $m$ floating on a flowing river. The maximum mass of the block is related to the speed of the river flow $v$, acceleration due to gravity $g$, and the density of the block $\rho$ such that $m_{\max} = k v^x g^y \rho^z$ ($k$ is a constant). The values of $x, y$, and $z$ should then respectively be:
(Mass of the spongy block is assumed to vary due to absorption of water by it)

Which of the following is a dimensional constant?

$A$ body of mass $m$ is moved by a flowing river. The mass $m$ depends on the velocity of the river $v$,the density of water $\rho$,and the acceleration due to gravity $g$. Then $m \propto$ ?

The force $F$ is given by the equation $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?

The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$,its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,