The formula $X = 5YZ^2$, $X$ and $Z$ have dimensions of capacitance and magnetic field respectively. What are the dimensions of $Y$ in $SI$ units?
$[{M^{ - 2}}\,{L^0}\,{T^{ - 4}}\,{A^{ - 2}}]$
$[{M^{ - 3}}\,{L^{-2}}\,{T^8}\,{A^{ 4}}]$
$[{M^{ - 2}}\,{L^{-2}}\,{T^6}\,{A^3}]$
$[{M^{ - 1}}\,{L^{-2}}\,{T^4}\,{A^2}]$
If the buoyant force $F$ acting on an object depends on its volume $V$ immersed in a liquid, the density $\rho$ of the liquid and the acceleration due to gravity $g$. The correct expression for $F$ can be
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.
With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a(2t - 1)$ is
Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.
A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$
$(b)\;y=a \sin v t$
$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.