The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

Convert $1 \; \text{newton}$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force).

The displacement $y$ of a particle at a distance $x$ at time $t$ for a transverse wave is given by $y = a \sin(bt - cx)$,where $a, b,$ and $c$ are constants. The dimensions of $b/c$ are the same as those of:

$A$ modified gravitational potential is given by $V = -\frac{GM}{r} + \frac{A}{r^2}$. If the constant $A$ is expressed in terms of gravitational constant $G$,mass $M$,and velocity of light $c$,then from dimensional analysis,$A$ is:

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ and $\beta$ are:

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.