Answer to Question #169045 in Physics for Samuel Mkandawire

Question

1. Clearly explain the meaning of a physical quantity.

2. Briefly explain what is meant by a dimension.

3. From the following physical quantities, which pair has the same dimensions?

(i) moment of couple and work

(ii) force and power

(iii) latent heat and specific heat

(iv) work and power

4. Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of the oil is given by

𝜂=𝑃(𝑟2− 𝑥2)4𝑣𝑙

Where v is the velocity of oil at a distance x from the axis of the tube. Determine the dimensions of η.

5. The position x of a particle depends upon time t according to the equation x = at + bt2. Determine the dimensions and units of a and b. What are the physical quantities denoted by a and b?

6. The velocity v of a particle depends upon time t according to the relation

𝑣=𝑎𝑡+ 𝑏𝑡+𝑐

What are the dimensions of a, b and c?

2

7. Use the principle of homogeneity, check the correctness of the following equation

ℎ=2𝑇𝐶𝑜𝑠𝛽𝑟𝑑𝑔

where β is the angle of contact, d is the density of a liquid, r is the radius of the tube, g is acceleration due to gravity, h is the height of the liquid and T is the surface tension.

8. If the escape velocity depends upon;

(i) Acceleration due to gravity of the planet

(ii) The radius of the planet

Establish the relationship between them by dimensional analysis.

[Hint, 𝑣𝑒𝛼 𝑔𝑎𝑅𝑏]

9. In the equation (𝑃+𝑎𝑉2)(𝑉−𝑏)=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, determine the units of a and b.

10. The square of the speed v of an object undergoing acceleration a is a variable of a function a and the displacement S according to the expression given by

𝑣2=𝑘𝑎𝑚𝑆𝑛

What dimensions should k have in order for the expression to be dimensionally consistent?

Answer 1

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