(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 and Measurements 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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Class 11

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Units and Measurements

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Dimensional Analysis, Uses and Limitations

Which of the following operations can be performed on two physical quantities $A$ and $B$ if they possess different dimensions?

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The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

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Write the dimensions of $a / b$ in the relation $P = \frac{a - t^2}{bx}$; where $P$ is the pressure,$x$ is the distance,and $t$ is the time.

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The period of a body under $SHM$ is presented by $T = P^a D^b S^c$; where $P$ is pressure,$D$ is density,and $S$ is surface tension. The values of $a, b,$ and $c$ are:

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The velocity of a particle depends upon the time $t$ according to the equation $v = \sqrt{ab} + bt + \frac{c}{d + t}$. The physical quantities which are represented by $a, b, c$ and $d$,are in the following order:

Medium

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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

Which of the following operations can be performed on two physical quantities $A$ and $B$ if they possess different dimensions?

The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

Write the dimensions of $a / b$ in the relation $P = \frac{a - t^2}{bx}$; where $P$ is the pressure,$x$ is the distance,and $t$ is the time.

The period of a body under $SHM$ is presented by $T = P^a D^b S^c$; where $P$ is pressure,$D$ is density,and $S$ is surface tension. The values of $a, b,$ and $c$ are:

The velocity of a particle depends upon the time $t$ according to the equation $v = \sqrt{ab} + bt + \frac{c}{d + t}$. The physical quantities which are represented by $a, b, c$ and $d$,are in the following order:

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