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1.Units, Dimensions and Measurement
hard
If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimension as that the $\sqrt{\mathrm{uG}}$
APressure gradient per unit mass
BForce per unit mass
CGravitational potential
DEnergy per unit mass
(JEE MAIN-2024)
Solution
${[\mathrm{uG}]=\left[\left(\mathrm{M}^1 \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right)\left(\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right)\right]}$
${[\mathrm{uG}]=\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-4}\right]}$
${[\sqrt{\mathrm{uG}}]=\left[\mathrm{L}^1 \mathrm{~T}^{-2}\right]}$
Option $(2)$ is correct
${[\mathrm{uG}]=\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-4}\right]}$
${[\sqrt{\mathrm{uG}}]=\left[\mathrm{L}^1 \mathrm{~T}^{-2}\right]}$
Option $(2)$ is correct
Standard 11
Physics
