Properties Of Matter - Mechanics - Physics Previous Year Questions

Water flows in a streamline motion through a horizontal pipe of circular cross-section as shown in the figure. The pressure difference of water between $P$ and $Q$ is $15 \mathrm{Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40 \mathrm{~cm}^2$ and $20 \mathrm{~cm}^2$, respectively. The rate of flow of water through the pipe, in $\mathrm{cm}^3 \mathrm{~s}^{-1}$, is:

[Take density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ ]

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity ( $v$ ) with the ratio of density of spherical ball ( $\sigma$ ) to density of the liquid ( $\rho$ ), is best represented by: