If {E}, {L}, {m} and {G} denote quantities as energy, angular momentum, mass and constant of gravita

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1.Units, Dimensions and Measurement

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If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are

$\left[{M}^{0} {L}^{1} {T}^{0}\right]$

$\left[{M}^{-1} {L}^{-1} {T}^{2}\right]$

$\left[{M}^{1} {L}^{1} {T}^{-2}\right]$

$\left[{M}^{0} {L}^{0} {T}^{0}\right]$

(JEE MAIN-2021)

Solution

${E}={ML}^{2} {T}^{-2}$

${L}={ML}^{2} {T}^{-1}$

${m}={M}$

${G}={M}^{-1} {L}^{+3} {T}^{-2}$

${P}=\frac{{EL}^{2}}{{M}^{5} {G}^{2}}$

${[{P}]=\frac{\left({ML}^{2} {T}^{-2}\right)\left({M}^{2} {L}^{4} {T}^{-2}\right)}{{M}^{5}\left({M}^{-2} {L}^{6} {T}^{-4}\right)}={M}^{0} {L}^{0} {T}^{0}}$

Standard 11

Physics

If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then

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(IIT-1992)

With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a(2t – 1)$ is

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A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:

$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$

$(b)\;y=a \sin v t$

$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$

$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$

$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.

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easy

If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are

Solution

Similar Questions

If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then

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