A hypothetical equation is given as $\rho = a \sqrt{P} + bT^2$, where $\rho$ is density, $P$ is pressure, and $T$ is temperature. The dimensions of $\frac{a}{b}$ are:

If $x = a + bt^2$, where $x$ is in meters and $t$ is in seconds, what are the dimensions of $b$?

A highly advanced alien civilization uses a unit of mass called a 'glorp' and a unit of length called a 'blarp'. Their fundamental unit of time is the 'zorp'. They discover a fundamental law of physics relating force (F), mass (m), length (l), and time (t) expressed as $F = K m^a l^b t^c$, where K is a dimensionless constant. If the dimensions of force in their system are glorp\cdot blarp \cdot zorp^{-2}$, what are the values of a, b, and c?

If the equation $P = \frac{F}{A}$ is dimensionally homogeneous, where $P$ is pressure, $F$ is force, and $A$ is area, what are the dimensions of pressure?

Unit of magnetic moment is

Which of the following equations is dimensionally homogeneous?

If the speed $v$ of transverse waves on a stretched string depends on the tension $T$ in the string and the mass per unit length $μ$ of the string, which of the following is dimensionally consistent?

If ${u_1}\,and\,{u_2}$ are the units selected in two systems of measurement and ${n_1}\,and\,{n_2}$ their numerical values, then

Which of the following physical quantities has neither dimensions nor unit?

If the unit of length and force be increased four times, then the unit of energy is

Faraday is the unit of