Which of the following pairs of physical quantites does not have same dimensional formula ?

Options

A. Work and torque
B. Angular momentum and Planck's constant
C. Tension and surface tension
D. Impulse and linear mementum

Answer

C

Explanation

(a) Work = force `xx` distance = `["MLT"^(-2)]["L"]=["ML"^(2)"T"^(-2)]`
Torque = force `xx` distance = `["ML"^(2)"T"^(-2)]`
(b) Angular momentum = `mvr=["M"]["LT"^(-1)]["L"]=["ML"^(2)"T"^(-1)]`
Planck's constant `=(E)/(v)=(["ML"^(2)"T"^(-2)])/(["T"^(-1)])=["ML"^(2)"T"^(-1)]`
(c) Tension =force = `["MLT"^(-2)]`
Surface tension = `("force")/("length")=(["MLT"^(-2)])/(["L"])=["ML"^(0)"T"^(-2)]`
(d) Impulse = force `xx` time = `["MLT"^(-2)]["T"]=["MLT"^(-1)]`
Momentum = mass `xx` velocity = `["M"]["LT"^(-1)]=["MLT"^(-1)]`
Note : One should not be confused with the similer form tension in both the physical quantities-surface tension and tension. Dimensional formula for both of them is not same.