The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

Length is measured in metre and time in second as usual. But a new unit of mass is so chosen that G=1. This new unit of mass is equal to

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?

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:

Length is measured in metre and time in second as usual. But a new unit of mass is so chosen that G=1. This new unit of mass is equal to

One is equivalent to 931 MeV energy. The rest mass of electron is $9.1 imes {10^{ - 31}}kg$. the Mass equivalent energy is (1 amu = $= 1.67 imes {10^{ - 17}}kg$)

What will be the unit of time in that system in which the unit of length is metre, unit of mass is kg and unit of force is kg wt?

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

Which of the following units denotes the dimensions $\left[ {{\rm{M}}{{\rm{L}}^2}/{{\rm{Q}}^2}} \right],$, where Q denotes the electric charge?

Consider a new system of units in which c(speed of light in vacuum), h(Planck’s constant) and G(gravitational constant) are taken as fundamental units. Which of the following would correctly represent mass in this new system?

A calorie is a unit of heat and equal 4.2 J. Suppose we employ a system of units in which the unit of mass is $\alpha$ kg, the unit of length is $\beta$ metre and the unit of time is γ sec. In this new system. 1 calorie =