Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2023

PhysicsEasysingle choice

If the velocity of light $c$ , universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is:

Options:

Answer:

Solution:

If $E$ is energy, then

$[E] = [\frac{G m_{1} m_{2}}{r}]$

$[E] [r] = [G m_{1} m_{2}]$

Since $E = \frac{h c}{λ}$

$[\frac{h c}{λ}] [r] = [G m_{1} m_{2}] \Rightarrow \frac{[h c]}{[L]} [L] = [G] [M^{2}]$

(both $λ$ and $r$ have dimensions of length)

$∴ [\sqrt{\frac{h c}{G}}] = [M]$

Stream:JEESubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2023

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