Which of the following pairs have same dimensions ?

Options

A. Torque and Work
B. Angular momentum and work
C. Energy and young's modulus
D. Light year and Wavelength

Answer

(a,d)

Explanation

(a) As, Torque = Force xx perpendicular distance
`MLT^(-2)xxL = ML^2 T^(-2)`
Work = Force xx displacement
`=MLT^(-2) xx L= ML^2 T^(-2)`
Hence option (a) is correct.
(b) Angular momentum ` =m upsilon r`
`=M(LT^(-1) L = ML^2 T^(-1))`
Work = force xx displacement
`=MLT^(-2) xx L = ML^2 T^(-2)`
Hence option (b) is incorrect.
(c ) Energy= work `=ML^2 T^(-2)`
Young's modulus ` = ("Normal stress")/("Longitudinal strain")`
`=(FI)/(A xx Delta I) = (MLT^(-2).L)/(L^2xx L)` = ML^(-1) T^(-2)`
Hence option (c ) is incorrect.
(d) Light year = [L], Wavelength =[L]
Hence option (d) si correct.