The pair(s) of physical quantities that have the same dimensions, is (are)
Reynolds number and coefficient of friction
Latent heat and gravitational potential
Curie and frequency of a light wave
All of these
The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be
A beaker contains a fluid of density $\rho \, kg / m^3$, specific heat $S\, J / kg\,^oC$ and viscosity $\eta $. The beaker is filled upto height $h$. To estimate the rate of heat transfer per unit area $(Q / A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)$ and $\left( {\frac{1}{{\rho g}}} \right)$ when $\Delta \theta $ (in $^oC$) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(Q / A)$ is
A gas bubble from an explosion under water oscillates with a period proportional of $P^a\,d^b\,E^c$ where $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then $a,\,b$ and $c$ are
Match List $I$ with List $II$
LIST$-I$ | LIST$-II$ |
$(A)$ Torque | $(I)$ $ML ^{-2} T ^{-2}$ |
$(B)$ Stress | $(II)$ $ML ^2 T ^{-2}$ |
$(C)$ Pressure of gradient | $(III)$ $ML ^{-1} T ^{-1}$ |
$(D)$ Coefficient of viscosity | $(IV)$ $ML ^{-1} T ^{-2}$ |
Choose the correct answer from the options given below
Which of the following group have different dimension