GATE 2022 Mechanical Engineering PYQ

Question

A solid spherical bead of lead (uniform density = 11000 kg/m³) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 10^-3 kg∙m^-1∙s^-1). The coefficient of drag is given by $\rm C_D = \frac{24}{Re} $, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as $\rm D = (C_D) (0.5 \rho V^2) \left( \frac{\pi d^2}{4} \right), $ where ρ is the density of the liquid. Neglect the buoyancy force. Using g = 10 m/s², the velocity V is __________ m/s.

Accepted Answer

$\frac{1}{18}$

Answer

$\frac{1}{24}$

Answer

$\frac{1}{6}$

Answer

$\frac{1}{12}$