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Worksheet on Dimension Analysis and Error Analysis

It is extremely important for every student of class 11 to learn dimensional formulas of following 40 quantities.


Q1) Write the dimensional formula of following quantities:


1) Mass

2) Length

3) Time

4) Velocity / speed

5) Acceleration

6) Acceleration due to gravity

7) Centripetal acceleration

8) Force

9) Tension

10) Surface tension

11) Pressure

12) Stress

13) Strain

14) Work

15) Energy

16) Torque

17) Moment of force

18) Moment of momentum

19) Displacement

20) Distance

21) Time

22) Time period

23) Universal gas constant

24) Universal gravitational constant

25) Planks constant

26) Frequency

27) Angle

28) Power

29) Velocity gradient

30) Impulse

31) Momentum

32) Angular velocity

33) Angular momentum

34) Critical velocity

35) Terminal velocity

36) Escape velocity

37) Mass density

38) Energy density

39) Modulus of elasticity

40) Efficiency



Q2) Find the number of significant figure in each of the following: (a) 7.3

(b) 162.5 m

(c) 306 g

(d) 3.57 m

(e) 7.005 kg

(f) 0.045 km

(g) 0.00234 l

(h) 82.030 mg.


(i) 20.020200 g

(j) 30.00 km

(k) 2.500 ml

(l) 60.001

Q3) Round off each of the following correct up to 3 significant figures: (a) 56.4517 g

(b) 5.20763 kg

(c) 33.311 km

(d) 50.001 cm

(e) 0.0012485 m

(f) 0.0013020 l



Q4) Round off: (a) 15.256 g correct to the three significant figures. (b) 0.00838 mg correct to the two significant figures.

(c) 0.004509 g correct to the one significant figures.

(d) 29.404 mm correct to the four significant figures.

(e) 22.311 km correct to the four significant figures.

(f) 3.0921 kg correct to the two significant figures.

(g) 0.003519 mm correct to the one significant figures.




Q5) Zero error of an instrument introduces :


a) Systematic errors

b) Random errors

c) Both

d) None of these



Q6) If error in measuring diameter of a circle is 4 %, the error in circumference of the circle would be :-


a) 2%

b) 8%

c) 4%

d) 1%



Q7) Percentage error in measuring the radius and mass of a solid sphere are 2% & 1% respectively. Then error in measurement of moment of inertia about to its diameter is :-


a) 3 %

b) 6 %

c) 5 %

d) 4 %



Q8) The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of kinetic energy obtained by measuring mass and speed ?


a) 11 %

b) 8 %

c) 5 %

d) 1 %



Q9) While measuring acceleration due to gravity by a simple pendulum a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of the time period. His percentage error in the measurement of the value of g will be -


a) 2 %

b) 4 %

c) 7 %

d) 10 %



Q10) When a copper sphere is heated, maximum percentage change will be observed in -


a) radius

b) area

c) volume

d) none of these



Q11) If voltage across a bulb rated 220 Volt 100 Watt drops by 2.5% of its rated value, the percentage of the rated value of which the power would decrease is :-


a) 5%

b) 10%

c) 20%

d) 2.5%



Q12) If a set of defective weights are used by a student to find the mass of an object using a physical balance, a large number of reading will reduce :-


a) random error

b) random as well as systematic error

c) systematic error

d) neither random nor systematic error



Q13) Which of the following quantity is unitless?


a) Velocity gradient

b) Pressure gradient

c) Displacement gradient

d) Force gradient



Q14) The fundamental unit which has same power in the dimensional formula of surface tension and co-efficient of viscosity is :


a) Mass

b) Length

c) Time

d) None



Q15) Which of the following does not have the dimensions of force ?


a) Potential gradient

b) Energy gradient

c) Weight

d) Rate of change of momentum



Q16) Which of the following is incorrect statement


a) A dimensionally correct equation may be correct

b) A dimensionally correct equation may be incorrect

c) A dimensionally incorrect equation may be correct

d) A dimensionally incorrect equation is incorrect



Q17) A dimensionless quantity:


a) Never has a unit

b) Always has a unit

c) May have a unit

d) Does not exist



Q18) A unitless quantity:


a) Does not exist

b) Always has a nonzero dimension

c) Never has a nonzero dimension

d) May have a nonzero dimension



Q19) Which of the following is incorrect ?


a) All derived quantities may be represented dimensionally in terms of the base quantities

b) A base quantity cannot be represented dimensionally in terms of other base quantities

c) The dimension of a derived quantity is never zero in any base quantity

d) The dimension of a base quantity in other base quantities is always zero.



Q20) Two physical quantities of which one is a vector and the other is a scalar having the same dimensional formula are :


a) Work and energy

b) Torque and work

c) Impulse and momentum

d) Power and pressure



Q21) Which of the following pairs does not have similar dimensions?


a) Tension and surface tension

b) Stress and pressure

c) Planck's constant and angular momentum

d) Angle and strain



Q22) The period of oscillation of a simple pendulum in an experiment is recorded as 2. 63s, 2.56s, 2.42s, 2.71s and 2.80s respectively. The average absolute error is


a) 0.1s

b) 0.11s

c) 0.01s

d) 1.0s





Answers:

2) (a) 2

(b) 4

(c) 3

(d) 3

(e) 4

(f) 2 (g) 3

(h) 5

(i) 8

(j) 4

(k) 4

(l) 5

3) (a) 56.5 g (b) 5.21 kg (c) 33.3 km (d) 50.0 cm (e) 0.00125 m (f) 0.00130 l

4) (a) 15.3 g (b) 0.0084 mg

(c) 0.005 g (d)29.40 (e) 22.31 km (f) 3.1 kg (g) 0.004 mm 5) a

6) c

7) c

8) b

9) c

10) c

11) a

12) a

13) c

14) a

15) a

16) c

17) c

18) c

19) c

20) b

21) a

22) b





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