Dimensions of frac{α}{β} in equation F=frac{α-t^2}{β v^2} , where F is force, v is velocity and

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

medium

The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........

A

$\left[ MLT ^{-1}\right]$

B

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

C

$\left[M L^3 T^{-4}\right]$

D

$\left[ ML ^2 T ^{-4}\right]$

Solution

(c)

$F=\frac{\alpha-t^2}{\beta v^2}$

Dimensionally, $\alpha=\left[ T ^2\right]$

$\left[M L T^{-2}\right]=\frac{\left[ T ^2\right]}{\beta\left[L^2 T^{-2}\right]}$

$\beta=\frac{ T ^2}{\left[ MLT ^{-2} \cdot L ^2 T ^{-2}\right]}$

$\Rightarrow \beta=\left[ M ^{-1} L ^{-3} T ^6\right]$

Dimensions of $\frac{\alpha}{\beta}=\frac{ T ^2}{ M ^{-1} L ^{-3} T ^6}=\left[ ML ^3 T ^{-4}\right]$

Standard 11

Physics

Share

Similar Questions

The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is

hard

In a particular system the units of length, mass and time are chosen to be $10\;cm , 10 \;g$, and $0.1\;s$ respectively. The units of force in this system will be equal to?

medium

A gas bubble from an explosion under water oscillates with a period proportional of $P^a\,d^b\,E^c$ where $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then $a,\,b$ and $c$ are

hard

Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then

medium

(IIT-1998)

A length-scale $(l)$ depends on the permittivity $(\varepsilon)$ of a dielectric material. Boltzmann constant $\left(k_B\right)$, the absolute temperature $(T)$, the number per unit volune $(n)$ of certain charged particles, and the charge $(q)$ carried by each of the particless. Which of the following expression($s$) for $l$ is(are) dimensionally correct?

($A$) $l=\sqrt{\left(\frac{n q^2}{\varepsilon k_B T}\right)}$

($B$) $l=\sqrt{\left(\frac{\varepsilon k_B T}{n q^2}\right)}$

($C$)$l=\sqrt{\left(\frac{q^2}{\varepsilon n^{2 / 3} k_B T}\right)}$

($D$) $l=\sqrt{\left(\frac{q^2}{\varepsilon n^{1 / 3} k_B T}\right)}$

normal

(IIT-2016)