In which of the following pairs, the two physical quantities have different dimensions?

Options

A. Planck's constant and angular momentum
B. Impulse and linear momentum
C. Moment of inertia and moment of a force
D. Energy and torque

Answer

C

Explanation

(a) Planck's sconstant = `("Energy")/("Frequency")=(["ML"^(2)"T"^(-2)])/(["T"^(-1)])=["ML"^(2)"T"^(-1)]`
Angular momentum = Moment of inertia `xx` Angular velocity
`" "=["ML"^(2)]xx["T"^(-1)]=["ML"^(2)"T"^(-1)]`
(b) Impulse = Force `xx` Time = `["MLT"^(-2)]["T"]=["MLT"^(-1)]` and linear momentum = Mass `xx` Velocity
`" "=["M"]["LT"^(-1)]=["MLT"^(-1)]`
(c) Moment of inertia = Mass `xx` `("Distance")^(2)`
`" "=["ML"^(2)]=["M"]["L"^(2)]`
and moment of force = Force `xx` Distance
`" "=["MLT"^(-2)]["L"]=["ML"^(2)"T"^(-2)]`
(d) Energy = `["ML"^(2)"T"^(-2)]` and torque = `["ML"^(2)"T"^(-2)]`