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

$A$ physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula $[M^{2a} L^{4b} T^{2c} K^d]$. Then the value of $\frac{a+b}{c+b}-d$ is

What is dimensional analysis? Write the limitations of dimensional analysis.

The equation of motion of a damped oscillator is given by $m \frac{d^2 x}{d t^2}+b \frac{d x}{d t}+k x=0$. The dimensional formula of $\frac{b}{\sqrt{k m}}$ is

Using dimensional analysis,the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

Consider an expression $Q V = k P T L^\alpha$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{-1} T^{-1}$. $k$ is a dimensionless constant. The value of the integer $\alpha$ is: