MCQ
The dimensional formula for $r.m.s.$ (root mean square) velocity is
  • ${M^0}L{T^{ - 1}}$
  • B
    ${M^0}{L^0}{T^{ - 2}}$
  • C
    ${M^0}{L^0}{T^{ - 1}}$
  • D
    $ML{T^{ - 3}}$

Answer

Correct option: A.
${M^0}L{T^{ - 1}}$
a
The dimensional formula for the $RMS$ velocity is same as the normal velocity.

So, dimension of $RMS$ velocity is $=\left[ M ^0 LT ^{-1}\right]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in the same vessel at temperature $T.$ The mean square of the velocity of molecules of gas $B$ is ${v^2}$ and the mean square of $x$ component of the velocity of molecules of gas $A$ is ${w^2}$. The ratio $\frac{{{w^2}}}{{{v^2}}}$ is
A copper rod of $88\; \mathrm{cm}$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is....$cm$

$( \alpha_{Cu}=1.7 \times 10^{-5}\; \mathrm{K}^{-1}$ and $\alpha_{Al}=2.2 \times 10^{-5} \;\mathrm{K}^{-1} ) $

Two parallel plate capacitors of capacity $C$ and $3\,C$ are connected in parallel combination and charged to a potential difference $18\,V$. The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant $9$. The final potential difference across the combination of capacitors will be $V$
A radio transmitter transmits at $830\, kHz$. At a certain distance from the transmitter magnetic field has amplitude $4.82\times10^{-11}\,T$. The electric field and the wavelength are respectively
Two masses $m_1$ and $m_2$ are connected by a string of length $l$. They are held in a horizontal plane at a height $H$ above two heavy plates $A$ and $B$ made of different material placed on the floor. Initially distance between two masses is $a < l$. When the masses are released under gravity they make collision with $A$ and $B$ with coefficient of restitution $0.8$ and $0.4$ respectively. The time after the collision when the string becomes tight is :- (Assume $H>>l$)
For photoelectric emission from certain metal the cutoff frequency is $\nu$. If radiation of frequency $2\nu$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be ($m$ is the electron mass)
A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by $30\,cm$ to focus the object again. The height of the liquid in the bucket is $..........\,cm$
A particle moving along the $X-$axis executes simple harmonic motion, then the force acting on it is given by

Where $A$ and $K$ are positive constants

The energy of a photon of light of wavelength $450 nm$ is
Taking into account of the slgnificant figures, what is the value of $9.99\, m -0.0099\, m ?$