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Q. A bird of mass 1.23 kg is able to hover by imparting a downward velocity of 10 m/s uniformly to air of density $ \rho kg/{{m}^{3}} $ over an effective area $ 0.1{{m}^{2}} $ If the acceleration due to gravity is $ 10.m/{{s}^{2}}, $ then the magnitude of $ \rho $ is in $ kg/{{m}^{3}} $ :

EAMCETEAMCET 2003

Solution:

Given: Mass of bird m = 1.25 kg Velocity v =10m/s Area, $ A=0.1\,{{m}^{2}} $ The density is given by $ \rho =\frac{Mass}{Volume}=\frac{M}{V}=\frac{M}{Av} $ $ (\because V=Av) $ $ =\frac{12.3}{0.1\times 10}=1.23\,kg/{{m}^{3}} $