1. The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?
2. Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius.
3. Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively.
4. The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position s = kamtn, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can this analysis give the value of k?
5. Which of the following equations are dimensionally correct? (a) vf = vi + ax
(b) y = (2 m)cos(kx), where k = 2 m–1.
6. Newton’s law of universal gravitation is represented by
Here F is the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg·m/s2. What are the SI units of the proportionality constant G?
7. A worker is to paint the walls of a square room 8.00 ft high and 12.0 ft along each side. What surface area in square meters much she cover?
8. The volume of a wallet is 8.50 in.3 Convert this value to m3, using the definition 1 in. = 2.54 cm.
9. A rectangular building lot is 100 ft by 150 ft. Determine the area of this lot in m2.
10. A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm3. From these data, calculate the density of lead in SI units (kg/m3).
11. An ore loader moves 1 200 tons/h from a mine to the surface. Convert this rate to lb/s, using 1 ton = 2 000 lb.
12. How many significant figures are in the following numbers? (a) 78.9 [pic] 0.2, (b) 3.788 ( 109, (c) 2.46 ( 10–6,...