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1.

The diameter of ball A is half that of ball B. What will be their ratio of their terminal velocities in water?

Answer»

The terminal velocity is directly proportional to the square of radius of the ball, therefore the ratio of terminal velocities will be 1:4.  
Discussion
2.

What is terminal velocity? What is the terminal velocity of a body in a freely falling system?

Answer»

It is the maximum constant velocity acquired by the body while falling freely in a viscous medium. In a freely falling system, g = 0. Therefore, the terminal velocity of the body will also be zero. 
Discussion
3.

A viscometer (an instrument used to study characteristics of a non-ideal fluid) consists of a flat plate and a rotating cone. The cone has a large apex angle and the angle `theta` shown in figure is very small (typically less than `0.5^(@)` ). The apex of the cone just touches the plate and a liquid fills the narrow gap between the plate and the cone. The cone has a base radius R and is rotated with constant angular speed `omega`. Consider the liquid to be ideal and take its coefficient of viscosity to be `eta`. Calculate the torque needed to drive the cone.

Answer» Correct Answer - `(2pietaomegaR^(3))/(3sintheta)~=(2pietaomegaR^(3))/(3theta)`
Discussion
4.

A vertical steel rod has radius a. The rod has a coat of a liquid film on it. The liquid slides under gravity. It was found that the speed of liquid layer at radius r is given by `v=(rhogb^(2))/(2eta)ln((r)/(a))-(rhog)/(4eta)(r^(2)-a^(2))` Where b is the outer radius of liquid film, `eta` is coefficient of viscosity and `rho` is density of the liquid. (i) Calculate the force on unit length of the rod due to the viscous liquid? (ii) Set up the integral to calculate the volume flow rate of the liquid down the rod. [you may not evaluate the integral]

Answer» Correct Answer - (i)`pirhoga^(2)[((b)/(a))^(2)-1]` (ii)`Q=int_(a)^(b)"v. 2"pirdr`
Discussion
5.

The coefficient of viscosity `eta` of a gas depends on mass of the gas molecule, its effective diameter and its average speed. It is known that diameter of helium atom is `2.1xx10^(-10)` m and its coefficient of viscosity, at room temperature is `2.0 xx 10^(-5)` kg `m^(-1)s^(-1)`. Estimate the effective diameter of `CO_(2)` molecule if it is known that `eta` at room temperature for `CO_(2)` is `1.5 xx 10^(-5)` kg `m^(-1)s^(-1)`.

Answer» Correct Answer - `4.4xx10^(-10)m`
Discussion
6.

A near surface earth satellite is in the shape of a sphere of radius r. It encounters cosmic dust in its path. The viscous force experienced by the satellite follows stoke’s law. The coefficient of viscosity is `eta`. Mass and radius of the earth are M and R respectively. (a) Calculate the power of the rocket engine that must be put on to keep the satellite moving as usual. (b) Calculate the equilibrium temperature of the surface of the satellite assuming that it radiates like a black body and no outer radiation falls on it. Assume that the heat generated due to viscous force is absorbed completely by the satellite body.

Answer» Correct Answer - (a) `(6piGMeter)/(R)` (b) `[(3etaGM)/(2sigmarR)]`
Discussion