JEE MAIN - Physics (2005 - No. 53)
Out of the following pair, which one does NOT have identical dimensions is
angular momentum and Planck's constant
impulse and momentum
moment of inertia and moment of a force
work and torque
Magyarázat
Moment of inertia, I = Mr2
$$\therefore$$ [I] = [ML2]
Moment of force, $$\overrightarrow \tau = \overrightarrow r \times \overrightarrow F $$
$$\therefore$$ $$[\overrightarrow \tau ]$$ = $$[L][ML{T^{ - 2}}]$$ = $$[ML^{ 2}{T^{ - 2}}]$$
$$\therefore$$ [I] = [ML2]
Moment of force, $$\overrightarrow \tau = \overrightarrow r \times \overrightarrow F $$
$$\therefore$$ $$[\overrightarrow \tau ]$$ = $$[L][ML{T^{ - 2}}]$$ = $$[ML^{ 2}{T^{ - 2}}]$$