## Unit – I E |

## Numerical Problems on System of Units: Numerical Problems

- Use standard prefixes used in S.I. system to express following quantities

a) 10^{6}phones b) 10^{-6}phones c) 10^{12}cows d) 10^{-9}monkeys e) 10^{-12}birds f)12×10^{-9}dogs g) 34 x 10^{3}boys Numerical Problems - Calculate number of kilometers in 20 miles using the conversion factors a mile = 5280 ft, 1 ft = 12 in, 1 in = 2.54 cm, 1 m = 100 cm, 1 km = 1000 m.
- Calculate the number of light years in one metre.
- Express 1 parsec in terms of light year Numerical Problems
- The mass of an electron is 9.1 x 10
^{-31}kg. How many electrons would make 1 kg? - The mass of an electron is 9.1 x 10
^{-31}kg. How many electrons would make 1 g? - The mass of a proton is 1.67 x 10
^{-27}kg. How many protons would make 1 g? - Express the distance between the sun and earth in parsec and light year.
- Derive the S.I. unit of joule (J) in terms of fundamental units.
- A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the earth in terms of a new unit if it takes 8 minutes and 20 seconds to cover the distance
- If x = a + bt + ct
^{2}, where x is in metres and t is in seconds. Find units of a, b and c. - Will the measure of a physical quantity depend on the system of units used?

### Answers:

- a) 1 Mphones b) 1μphones c) Tcows d) nmonkeys e) pbirds f) 12 ndogs g) 34 kboys
- 32.187 km
- 1.057 x 10
^{-16}light year - 3.256 light years
- 1.1 x 10
^{30} - 1.1 x 10
^{27} - 5.99 x 10
^{23} - 4.857 x 10
^{-6}parsec, 1.581 x 10^{-6}light year - kg m
^{2}s^{-2} - 500 new units
- unit of a = m, unit of b = m/s, unit of c = m/s2.