KVPY2017PhysicsUnits and Dimensions
Stoke's law states that the viscous drag force F experienced by a sphere of radius a, moving with a speed V through a fluid with coefficient of viscosity , is given by F=6 inav. If this fluid is flowing through a cylindrical pipe of radiusr, leng th / and a pressure difference of Pacross its two ends, then the volume of water V which flows through the pipe in time t can be written as V t =k ( P )^ a ^ b r^ c , where
Options
- Aa=1, b=-1, c=4
- Ba=-1, b=1, c=4
- Ca=2, b=-1, c=3
- Da=1, b=-2, c=-4
Correct answer
A. a=1, b=-1, c=4
Step-by-step solution
array l V t =k ( P )^ a ^ b ^ c [r]=L ;[l]=L [P]=M L⁻¹ T⁻² ;[ ]=M L⁻¹ T⁻¹ [ ~V ]=L³ [t]=T array By calculation a=1 ; b=-1 ; c=4