WORKSHEET#1 UNITS AND MESUREMENT
1. If the unit of force is 100N, unit of length is 10m and unit of time is 100s. What is the unit of Mass
in this system of units? 105kg.
2. Using dimensions convert (a) 1 newton into dynes (b) 1 erg into joules.
3. The magnitude of force experienced by an object moving with speed v is given by F = kv2. Find
Dimensions of k.
4. Give limitations of dimensional analysis.
5. For Determination of g using simple pendulum, measurements of length and time period are
required. Error in the measurement of which quantity will have a larger effect on the value of g thus obtained. What is done to minimise error?
6. Describe the Parallax Method for the determination of the distance of a nearby star from the earth.
7. Define the following units :(i) Lightyear (ii) Parsec(iii) Astronomical unit (Au)
8. Distinguish between the terms precision and accuracy of a measurement.
(i) absolute error (ii) mean absolute error(iii) relative error (iv) percentage error
(v) random error
10. Determine the number of light years in one metre. 1.057 × 10-16 Iy
11. The sides of a rectangle are (10..5 ± 0.2) cm and (5.2 ± 0.1) cm. Calculate its perimeter with error
limits. (31.4 ± 0.6) cm.
12. The mass of a box measured by a grocer’s balance is 2.3 kg. Two gold
pieces 20.15 g and 20.17 g are added to the box.
(i) What is the total mass of the box? 2.3 kg
(ii) The difference in masses of the pieces to correct significant figures. 0.02 g
13. 5.74 g of a substance occupies 1.2 cm3. Express its density to correct significant figures. 4.8 g/cm3.
14. If displacement of a body s = (200 ± 5) m and time taken by it t = (20 +0.2) s, then
find the percentage error in the calculation of velocity. 3.5%
15. If the error in the measurement of mass of a body be 3% and in the measurement of velocity be
2%.What will be the maximum possible error in the calculation of kinetic energy. 7%
16. The length of a rod as measured in an experiment was found to be 2.48m, 2.46m, 2.49m, 2.50m and 2.48m. Find the average length, absolute error and percentage error. Express the result with error
limit. (2.48 ± 0.01)m (2.48m ± 0.40%)
17. A physical quantity is measured as Q = (2.1 ± 0.5) units. Calculate thepercentage error in (1) Q2 (2) 2Q. 48% and 24%
18. When the planet Jupiter is at a distance of 824.7 million km from the earth, its angular diameter is
measured to be 35.72¢¢ of arc. Calculate diameter of Jupiter. 1.4287 × 105 km
19. A laser light beamed at the moon takes 2.56s and to return after reflection at the moon.s surface.
What will be the radius of lunar orbit. 3.84 × 108 m.
(i) 3 m/s.-2 to km/ h-.2 3.9 × 104 km h-.2
(ii) G = 6.67 × 10.-11 N m2 kg-2 to cm3 g-1 s-2 6.67 × 10-8 g-1 cm3 s-2.
21. A calorie is a unit of heat or energy and it equals 4.2 J where 1J = 1 kg m2s-2. Suppose we employ a
system of units in which unit of mass is a kg, unit of length is b m, unit of time gs. What will be
magnitude of calorie in terms of this new system. n2 = 4.2 a-1 b-2 g2
22. The escape velocity v of a body depends on.
(i) the acceleration due to gravity g of the planet,
(ii) the radius R of the planet. Establish dimensionally the relation for the escape
23. The frequency of vibration of a string depends of on, (i) tension in the string (ii) mass
per unit length of string, (iii) vibrating length of the string. Establish dimensionally the
relation for frequency.
24. One mole of an ideal gas at STP occupies 22.4 L. What is the ratio of
molar volume to atomic volume of a mole of hydrogen? Why is the ratio
so large. Take radius of hydrogen molecule to be 1ºA. 104 This ratio is large because actual size of gas molecule is negligible incomparison to the inter molecular separation.
25. Derive an expression for the centripetal force F acting on a particle of
mass m moving with velocity v in a circle of radius r.
26. The error in the measurement of radius of a sphere is 2%. What would be
the error in :
(a) Volume of sphere
(b) Surface area of sphere.