JEE MAIN - Physics (2020 - 4th September Evening Slot - No. 7)
A quantity x is given by $$\left( {{{IF{v^2}} \over {W{L^4}}}} \right)$$ in terms of moment of inertia I, force F, velocity v, work W and
Length L. The dimensional formula for x is same as that of :
Coefficient of viscosity
Force constant
Energy density
Planck's constant
Explanation
x = $$\left( {{{IF{v^2}} \over {W{L^4}}}} \right)$$
$$ \therefore $$ [x] = $${{\left[ {M{L^2}} \right]\left[ {ML{T^{ - 2}}} \right]{{\left[ {L{T^{ - 1}}} \right]}^2}} \over {\left[ {M{L^2}{T^{ - 2}}} \right]{{\left[ L \right]}^4}}}$$
= [ML-1T-2]
= [Energy density]
$$ \therefore $$ [x] = $${{\left[ {M{L^2}} \right]\left[ {ML{T^{ - 2}}} \right]{{\left[ {L{T^{ - 1}}} \right]}^2}} \over {\left[ {M{L^2}{T^{ - 2}}} \right]{{\left[ L \right]}^4}}}$$
= [ML-1T-2]
= [Energy density]
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