The value of gravitational acceleration in the $C.G.S.$ system is $980 \; cm/s^2$. Find the value of $g$ in the $M.K.S.$ system.

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)

An expression of energy density is given by $u = \frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$,where $\alpha, \beta$ are constants,$x$ is displacement,$k$ is Boltzmann constant,and $t$ is the temperature. The dimensions of $\beta$ will be.

In the equation $(P+\frac{a}{V^2})(V-b)=RT$,where $P$ is pressure,$V$ is volume,$T$ is temperature,$R$ is universal gas constant,and $a$ and $b$ are constants. The dimensions of $a$ are

The velocity $v$ of a particle at time $t$ is given by $v = at + \frac{b}{t + c}$,where $a, b,$ and $c$ are constants. What are the dimensions of $a, b,$ and $c$ respectively?

In the $CGS$ system,the magnitude of the force is $100 \ dynes$. In another system where the fundamental physical quantities are $kilogram$,$meter$,and $minute$,the magnitude of the force is: