(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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Class 11 Questions

Class 11

Physics Questions

Chapter

Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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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Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

Medium

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Why does the concept of dimension have basic importance?

Easy

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Planck's constant $(h)$,speed of light in vacuum $(c)$,and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

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If the relationship between velocity,acceleration,and force in two systems is given by $v_2 = \frac{\alpha^2}{\beta} v_1$,$a_2 = \alpha \beta a_1$,and $F_2 = \frac{F_1}{\alpha \beta}$,then what is the relationship between mass,length,and time?

Difficult

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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

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.

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

Why does the concept of dimension have basic importance?

Planck's constant $(h)$,speed of light in vacuum $(c)$,and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

If the relationship between velocity,acceleration,and force in two systems is given by $v_2 = \frac{\alpha^2}{\beta} v_1$,$a_2 = \alpha \beta a_1$,and $F_2 = \frac{F_1}{\alpha \beta}$,then what is the relationship between mass,length,and time?

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