7. (a). The standard kilogram is a platinum-iridium cylinder 39 mm in height and 39 mm in diameter. What is the density of the material? (b). Acceleration due to gravity is given as 9.8m/s2. What is its value in mm/ps2? (c). A liquid has a density of 6 kg/m3. What is the density of the liquid in g/mm3? (d). The density of lead is 11.3 ��њ3. What is this value in kilograms per cubic meter?
(a) To find the density of the material, we need to divide its mass by its volume. However, the given information only provides the dimensions of the cylinder, not its mass. Therefore, we cannot calculate the density without additional information about the mass.
(b) To convert the acceleration due to gravity from m/s^2 to mm/ps^2, we need to convert the units. There are 1000 millimeters (mm) in a meter (m), and 1000 picoseconds (ps) in a second (s). Therefore, we can use the following conversion:
1 m/s^2 = 1000 mm/s^2
1 s^2 = 1000 ps^2
So, to convert 9.8 m/s^2 to mm/ps^2, we can multiply by the conversion factors:
9.8 m/s^2 * (1000 mm/s^2 / 1 m/s^2) * (1 s^2 / 1000 ps^2) = 9.8 * 1000 * 1 /1000 = 9.8 mm/ps^2
Therefore, the value of acceleration due to gravity in mm/ps^2 is 9.8 mm/ps^2.
(c) To convert the density of a liquid from kg/m^3 to g/mm^3, we need to convert the units. There are 1000 grams (g) in a kilogram (kg), and 1 million cubic millimeters (mm^3) in a cubic meter (m^3). Therefore, we can use the following conversion:
1 kg/m^3 = 1000 g/m^3
1 m^3 = 1,000,000 mm^3
So, to convert 6 kg/m^3 to g/mm^3, we can multiply by the conversion factors:
6 kg/m^3 * (1000 g/m^3 / 1 kg/m^3) * (1 mm^3 / 1,000,000 m^3) = 6 * 1000 / 1,000,000 = 0.006 g/mm^3
Therefore, the density of the liquid in g/mm^3 is 0.006 g/mm^3.
(d) The density of lead is given as 11.3 kg/m^3. No conversion is needed in this case since the density is already in kilograms per cubic meter.
Therefore, the density of lead is 11.3 kg/m^3.