Question Video: Quantities and Units in Mechanics Mathematics

Which of the following is false? [A] 72 km/h = 20 m/s [B] 3 km/min = 50 cm/s [C] 15 m/s = 54 km/h [D] 42 m/min = 70 cm/s

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Video Transcript

Which of the following is false? (a) 72 kilometers per hour equals 20 meters per second. (b) Three kilometers per minute equals 50 centimeters per second. (c) 15 meters per second equals 54 kilometers per hour. Or (d) 42 meters per minute equals 70 centimeters per second.

To verify each equation, we need to convert the units on one side of the equation into the units on the other side of the equation. Let’s convert the units from the left-hand side of each equation into the units on the right-hand side of each equation and then compare the coefficients to see if they are true or false.

So, starting with (a), we need to convert kilometers into meters and hours into seconds. One kilometer is equal to 1000 meters, and one hour is equal to 3600 seconds. We therefore have 72 kilometers per hour equals 72 times 1000 meters per 3600 seconds. It can be helpful to write these as fractions so we can see the multiplication and division more clearly. So we have 72000 meters divided by 3600 seconds. Simplifying this, we obtain 20 meters divided by one second, or 20 meters per second. Therefore, equation (a) is true.

Next, for equation (b), we need to convert kilometers into centimeters and minutes into seconds. One kilometer equals 1000 meters. So in centimeters, one kilometer is 100000 centimeters, or 10 to the five centimeters. And similarly, one minute equals 60 seconds. Therefore, we have three kilometers per minute equals three times 10 to the five centimeters per 60 seconds. Simplifying this fraction, we get three kilometers per minute equals 5000 centimeters per second. Therefore, the false equation is (b) three kilometers per minute equals 50 centimeters per second.