If momentum $(P),$ area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional formula for energy is :
- [JEE MAIN 2020]
- A$\left[ PA ^{-1} T ^{-2}\right]$
- B$\left[ PA ^{1 / 2} T ^{-1}\right]$
- C$\left[ P ^{2} AT ^{-2}\right]$
- D$\left[ P ^{1 / 2} AT ^{-1}\right]$
Similar Questions
$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-
$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-
Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as
Using dimensional analysis, the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as
- [KVPY 2017]
A calorie is a unit of heat or energy and it equals about $4.2\; J$ where $1 \;J =1\; kg \,m ^{2} \,s ^{-2}$ Suppose we employ a system of units in which the unit of mass equals $\alpha\; kg$, the unit of length equals $\beta\; m$, the unit of time is $\gamma$ $s$. Show that a calorie has a magnitude $4.2 \;\alpha^{-1} \beta^{-2} \gamma^{2}$ in terms of the new units.
The quantity $X = \frac{{{\varepsilon _0}LV}}{t}$: ${\varepsilon _0}$ is the permittivity of free space, $L$ is length, $V$ is potential difference and $t$ is time. The dimensions of $X$ are same as that of
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- [IIT 2001]
In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equation$(s)$ is(are)
$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$
In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equation$(s)$ is(are)
$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$
- [IIT 2015]