(B) The dimensional formula for energy $E$ is $[M^1 L^2 T^{-2}]$.Given the relation $E = m^x \ell^y f^z$,we write the dimensional equation:$[M^1 L^2 T

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(B) The dimensional formula for energy $E$ is $[M^1 L^2 T^{-2}]$.Given the relation $E = m^x \ell^y f^z$,we write the dimensional equation:$[M^1 L^2 T^{-2}] = [M]^x [L]^y [T^{-1}]^z$$[M^1 L^2 T^{-2}] = [M^x L^y T^{-z}]$Comparing the powers of $M, L,$ and $T$ on both sides:For $M$: $x = 1$For $L$: $y = 2$For $T$: $-z = -2 \Rightarrow z = 2$Therefore,$x + y + z = 1 + 2 + 2 = 5$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

In a nuclear power plant,the energy released depends on the mass of the uranium sample $(m)$,the length of the oscillator $(\ell)$,and the frequency $(f)$ of oscillation as $E = m^{x} \ell^{y} f^{z}$. Then,what is the value of $x + y + z$?

A
$1$
B
$5$
C
$2$
D
None of these

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

An experiment measures quantities $a, b,$ and $c$ and then $x$ is calculated from $x = \frac{a^{1/2} b^2}{c^3}.$ If the percentage errors in $a, b,$ and $c$ are $\pm 1\%, \pm 3\%,$ and $\pm 2\%$ respectively,then the percentage error in $x$ is:

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The energy $(E)$, angular momentum $(L)$, and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

DifficultAP EAMCET 2008

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$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

Medium

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Using dimensional analysis,the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

KVPY 2017

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If momentum $(P)$,area $(A)$ and time $(T)$ are taken to be the fundamental quantities,then the dimensional formula for energy is:

MediumJEE MAIN 2020

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In a nuclear power plant,the energy released depends on the mass of the uranium sample $(m)$,the length of the oscillator $(\ell)$,and the frequency $(f)$ of oscillation as $E = m^{x} \ell^{y} f^{z}$. Then,what is the value of $x + y + z$?

Similar Questions

An experiment measures quantities $a, b,$ and $c$ and then $x$ is calculated from $x = \frac{a^{1/2} b^2}{c^3}.$ If the percentage errors in $a, b,$ and $c$ are $\pm 1\%, \pm 3\%,$ and $\pm 2\%$ respectively,then the percentage error in $x$ is:

The energy $(E)$, angular momentum $(L)$, and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

Using dimensional analysis,the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

If momentum $(P)$,area $(A)$ and time $(T)$ are taken to be the fundamental quantities,then the dimensional formula for energy is:

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