The dimensions of physical quantity $X$ in the equation Force $ = \frac{X}{{{\rm{Density}}}}$ is given by

  • A

    ${M^1}{L^4}{T^{ - 2}}$

  • B

    ${M^2}{L^{ - 2}}{T^{ - 1}}$

  • C

    ${M^2}{L^{ - 2}}{T^{ - 2}}$

  • D

    ${M^1}{L^{ - 2}}{T^{ - 1}}$

Similar Questions

Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$, mass of the bob $(m)$ and acceleration due to gravity $(g)$. Derive the expression for its time period using method of dimensions.

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]

The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are

If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is

  • [JEE MAIN 2021]

If $\varepsilon_0$ is permittivity of free space, $e$ is charge of proton, $G$ is universal gravitational constant and $m_p$ is mass of a proton then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p{ }^2}$ is