The Total solution for NCERT class 6-12
A man walking briskly in rain with speed v mustslant his umbrella forward making an angle θ with the vertical. A studentderives the following relation between θ and v: tan θ = v andchecks that the relation has a correct limit: as v →0, θ→ 0, as expected. (We are assuming there is no strong wind and that the rainfalls vertically for a stationary man). Do you think this relation can becorrect? If not, guess the correct relation.
Answer: Incorrect;on dimensional ground
Dimension of R.H.S = M0 L1 T–1
Dimension of L.H.S = M0 L0 T0
( The trigonometric functionis considered to be a dimensionless quantity)
Dimension of R.H.S is not equal to the dimension of L.H.S. Hence,the given relation is not correct dimensionally.
To make the given relation correct, the R.H.S should also bedimensionless. One way to achieve this is by dividing the R.H.S by the speed ofrainfall.
Therefore, the relation reduces to
. This relation is dimensionally correct.