Problem 6: Carry out the following conversions;

(a) Calculate the density of 1.33 * 10-7 g cm-3 into kg m-3.

(b) Calculate a speed of 20 m s-1 in km h-1.

Solution

(a)                    Given data:       Density = 1.33*10-7 g cm-3

Required:          Convert the above value to kg m-3

Strategy: Convert centimeters to meters and grams to kilograms.

Precaution:

• In the given data 1.33 * 10-7 grams of the mass are contained in a volume of 1 cm3. We have to convert 1.33*10-7 grams to kilograms and 1 cm3 to m3.
• When a multiple of base unit is raised to a power, the power applies to the whole multiple, for example, 1 km2 = 1 (km)2 = 1(103m)2 = 1*106 m2. (see question (i) in other questions)

Now

Now use (A) and (B) to find the required relation.

This is the required expression.

b

Given data: velocity of 20 m/s
Required: convert to km/hr
Strategy: Convert meters to kilometers and seconds to hours.

We know that And Put the values of meter and second from equations (i) and (ii) in the given equation, This was required.