The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $\mathrm{h} / \sqrt{2 m E}$ The dimensional formula for Planck's constant is:

  • [JEE MAIN 2024]
  • A

    $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$

  • B

    $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$

  • C

    $\left[\mathrm{MLT}^{-2}\right]$

  • D

    $\left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$

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  • [IIT 2001]

Dimensional formula for volume elasticity is

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

  • [JEE MAIN 2015]

convert $1\; newton$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force) 

The dimensions of $C{V^2}$ matches with the dimensions of