For which of the following quantities does ratios are dimensionless?
(i) `("work")/("Energy")` (ii) `sintheta` (iii) `(Momentum)/(Time)`

Explanation

(i) Since work and energy both have the same dimensions `[ML^(2)T^(-2)]`, their ratio is a dimensionless quantity.
(ii) sin(i). Here I represents an angle.
An angle is the ratio of two lengths i.e. are length and radiys. Therefore `i` is dimensionless, hence sin(i) is dimesnionless.
(iii) `[("Momentum")/("Time")]=([MLT^(-1)])/([T])`
= `[MLT^(-2)]`
Hence, the given ratio is not dimensionless.