If Surface tension $(S)$, Moment of Inertia $(I)$ and Planck’s constant $(h)$, were to be taken as the fundamental units, the dimensional formula for linear momentum would be

  • [JEE MAIN 2019]
  • A

    $S^{1 /2} I^{1 /2} h^0$

  • B

    $S^{1 /2} I^{3 /2} h^{-1}$

  • C

    $S^{3 /2} I^{1 /2} h^0$

  • D

    $S^{1 /2} I^{1 /2} h^{-1}$

Similar Questions

Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?

  • [IIT 2023]

In the equation $y = pq$ $tan\,(qt)$, $y$ represents position, $p$ and $q$ are unknown physical quantities and $t$ is time. Dimensional formula of $p$ is

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$, where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are

  • [KVPY 2017]

If the units of force, energy and velocity are respectively $10\, N, 100\, J, 5\, m/s$, then  the units of length, mass and time will be

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is