If surface tension is defined as force per unit length which of the following quantities will have the same units as surface tension ?

Options

A. `Work `xx ` volume `xx` speed`
B. `(" Work " xx "velocity ")/("volume ")`
C. `("work " xx " velocity ")/("rate of change of volume ")`
D. `("work ")/("time ") xx ("volume")/("velocity")`

Answer

D

Explanation

`2N =1 N_(1) =1 kg_(1) m_(1) s_(1)^(-2)`
` 2(m s^(-1)) =m_(1) s_(1)^(-1)`
`2s^(-1) =s_(1)^(-1)`
`:. 1 m=1 m_(1)`
`2 kg m s^(-2) =1 kg_(1)m_(1) s_(1)^(-2)`
`1kg_(1) =2kg .(1 m 1s^(-2))/(1m_(1) 1s_(1)^(-2))`
` 1kg_(1) =2kg .((1m)/(1m)) ((1s^(-1))/(1s_(1)^(-1)))^(+2)`
` =2 kg 1 xx ((1)/(2))^(2) =(2)/(4) kg=(1)/(2) kg`