Given that v is speed, r is radius and g is acceleration due to gravity. Which of following is dimen

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

medium

Given that $v$ is speed, $r$ is the radius and $g$ is the acceleration due to gravity. Which of the following is dimensionless

A

${v^2}/rg$

B

${v^2}r/g$

C

${v^2}g/r$

D

${v^2}rg$

Solution

(a) Angle of banking : $\tan \theta = \frac{{{v^2}}}{{rg}}$.

i.e. $\frac{{{v^2}}}{{rg}}$is dimensionless.

Standard 11

Physics

Share

Similar Questions

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $E]$ and $B$ stand for dimensions of electric and magnetic fields respectively, while $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $L$ and $T$ are dimensions of length and time respectively. All the quantities are given in $SI$ units.
($1$) The relation between $[E]$ and $[B]$ is
$(A)$ $[\mathrm{E}]=[\mathrm{B}][\mathrm{L}][\mathrm{T}]$
$(B)$ $[\mathrm{E}]=[\mathrm{B}][\mathrm{L}]^{-1}[\mathrm{~T}]$
$(C)$ $[\mathrm{E}]=[\mathrm{B}][\mathrm{L}][\mathrm{T}]^{-1}$
$(D)$ $[\mathrm{E}]=[\mathrm{B}][\mathrm{L}]^{-1}[\mathrm{~T}]^{-1}$
($2$) The relation between $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ is
$(A)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][\mathrm{L}]^2[\mathrm{~T}]^{-2}$
$(B)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][\mathrm{L}]^{-2}[\mathrm{~T}]^2$
$(C)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[\mathrm{~L}]^2[\mathrm{~T}]^{-2}$
$(D)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[\mathrm{~L}]^{-2}[\mathrm{~T}]^2$
given the answer question ($1$) and ($2$)

hard

(IIT-2018)

Planck's constant $(h),$ speed of light in vacuum $(c)$ and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length $?$

hard

(NEET-2016)

The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as

hard

(KVPY-2011)

It is estimated that per minute each $cm^2$ of earth receives about $2\ cal (1\ cal = 4.18\ J)$ of heat energy from the sun. This is called Solar constant. In $SI$ units the value is :-

medium

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

hard

(JEE MAIN-2015)