In the relation $y = a \cos (\omega t - kx)$,the dimensional formula for $k$ is

The expression given below shows the variation of velocity $(v)$ with time $(t)$,$v=At^2+\frac{Bt}{C+t}$. The dimension of $ABC$ is

Consider the efficiency of Carnot's engine is given by $\eta = \frac{\alpha \beta}{\sin \theta} \log_{e} \frac{\beta x}{k T}$,where $\alpha$ and $\beta$ are constants. If $T$ is temperature,$k$ is Boltzmann constant,$\theta$ is angular displacement and $x$ has the dimensions of length. Then,choose the incorrect option.

The time dependence of a physical quantity $P$ is given by $P = P_0 \exp(-\alpha t^2)$,where $\alpha$ is a constant and $t$ is time. The constant $\alpha$:

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

Heat produced in a current-carrying conducting wire depends on current $I$,resistance $R$ of the wire,and time $t$ for which the current is passed. Using these facts,obtain the formula for heat energy.