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1.Units, Dimensions and Measurement
hard
Given below are two statements :
$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.
$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.
In the light of the above statements, choose the correct answer from the options given below :
A Statement $I$ is true but Statement $II$ is false
BBoth Statement $I$ and Statement $II$ are false
C Both Statement $I$ and Statement $II$ are true
D Statement $I$ is false but Statement $II$ is true
(JEE MAIN-2024)
Solution
$ {[\mathrm{h}]=\mathrm{ML}^2 \mathrm{~T}^{-1}} $
$ {[\mathrm{~L}]=\mathrm{ML}^2 \mathrm{~T}^{-1}} $
$ {[\mathrm{P}]=\mathrm{MLT}^{-1}} $
$ {[\tau]=\mathrm{ML}^2 \mathrm{~T}^{-2}}$
(Here $\mathrm{h}$ is Planck's constant, $\mathrm{L}$ is angular momentum, $\mathrm{P}$ is linear momentum and $\tau$ is moment of force)
$ {[\mathrm{~L}]=\mathrm{ML}^2 \mathrm{~T}^{-1}} $
$ {[\mathrm{P}]=\mathrm{MLT}^{-1}} $
$ {[\tau]=\mathrm{ML}^2 \mathrm{~T}^{-2}}$
(Here $\mathrm{h}$ is Planck's constant, $\mathrm{L}$ is angular momentum, $\mathrm{P}$ is linear momentum and $\tau$ is moment of force)
Standard 11
Physics
