In the equation $y = x^2 \cos^2 \left( 2 \pi \frac{\beta \gamma}{\alpha} \right)$,the units of $x, \alpha, \beta$ are $m, s^{-1}$,and $(ms^{-1})^{-1}$ respectively. The units of $y$ and $\gamma$ are:

When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$, where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

The force $F$ on a sphere of radius $a$ moving in a medium with velocity $v$ is given by $F = 6\pi \eta av$. The dimensions of $\eta$ are

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.

If speed $(V)$,acceleration $(A)$,and force $(F)$ are considered as fundamental units,the dimension of Young's modulus will be

The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?