The Total solution for NCERT class 6-12
A man walking briskly in rain with speed┬аv┬аmustslant his umbrella forward making an angle ╬╕ with the vertical. A studentderives the following relation between ╬╕ and┬аv: tan ╬╕ =┬аv┬аandchecks that the relation has a correct limit: as┬аv┬атЖТ0,┬а╬╕тЖТ 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:┬аIncorrect;on dimensional ground
Dimension of R.H.S = M0┬аL1┬аTтАУ1
Dimension of L.H.S = M0┬аL0┬аT0
(┬аThe 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.