If pressure P , velocity V and time T are taken as fundamental physical quantities, dimensional form

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

medium

If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is

$P{V^2}{T^2}$

${P^{ - 1}}{V^2}{T^{ - 2}}$

$PV{T^2}$

${P^{ - 1}}V{T^2}$

Solution

$F\,\, = \,\,{P^\alpha }{v^\beta }{T^\gamma }$

$\left[ {{M^1}{L^1}{T^{ – 2}}} \right]\,\, = \,\,{\left[ {{M^1}{L^{ – 1}}{T^2}} \right]^\alpha }\,{\left[ {L{T^{ – 1}}} \right]^\beta }{\left[ T \right]^\gamma }$

$\,\,\left[ {{M^1}{L^1}{R^{ – 2}}} \right]\,\, = \,\,\left[ {{M^\alpha }{L^{ – \alpha \, + \;\beta }}{T^{ – 2\alpha – \beta + \gamma }}} \right]$

$\alpha \,\, = \,\,1\,;\,\, – \alpha \,\, + \;\,\beta \,\, = \,\,1\,$

$\beta \,\, = \,\,\,2,\,\,2 – 2\alpha \,\, – \,\,\beta \,\, + \;\,\gamma \,\, = – 2$

$\therefore \,\, – 2\,\, – \,\,2\,\, + \;\,\gamma \,\, = – 2\,\,$

$\,\gamma \,\, = \,\,2$

$ \Rightarrow \,\,F\,\, = \,\,P{v^2}{T^2}$

Standard 11

Physics

Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is

hard

If force $({F})$, length $({L})$ and time $({T})$ are taken as the fundamental quantities. Then what will be the dimension of density

hard

(JEE MAIN-2021)

The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be

medium

Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energy

medium

A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$

medium

If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is

Solution

Similar Questions

Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is

If force $({F})$, length $({L})$ and time $({T})$ are taken as the fundamental quantities. Then what will be the dimension of density

The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be

Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energy

A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$

Start a Free Trial Now