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CBSE Test Paper 01 Chapter 2 Units and Measurements
- The number of significant digits in 6.320 J is 1
a. 6 b. 4 c. 3 d. 5
- Newton is the SI unit of 1
a. acceleration b. work c. power d. force
- The dimensions of Kinetic energy is same as that of 1
a. Pressure b. Work c. Momentum d. Force
- A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance? 1
a. 500 b. 450 c. 600 d. 550
- The number of significant digits in 0.0006032 is 1
a. 4
b. 6 c. 5 d. 3
- Define S.I. unit of solid angle? 1
- How many light years make 1 parsec? 1
- Is it Possible to have length and velocity both as fundamental quantities? Why? 1
- The principle of 'parallax' in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth's orbit =. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1" (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1" (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters? 2
- The resistance R is the ratio of potential difference V and current I. What is the percentage error in R if V is (100 ± 5) V and I is (10 ± 2) A? 2
- The Sun's angular diameter is measured to be 1920". The distance r of the sun from
the earth is 1.496 1011 m. What is the diameter of the Sun? 2
- A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants? 3
CBSE Test Paper 01 Chapter 2 Units and Measurements
Answer
- b. 4 Explanation: There are three rules on determining how many significant figures are in a number:
Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant.
So keeping these rules in mind, there are 4 significant digit.
- d. force Explanation: The newton is the SI unit for force; it is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
- b. Work Explanation: Work
- a. 500 Explanation: Distance between the Sun and the Earth = Speed of light Time taken by light to cover the distance Given that in the new unit, speed of light = 1 unit Time taken, t = 8 min 20 s = 500 s Distance between the Sun and the Earth = 1 x 500 = 500 units
- a. 4 Explanation: There are three rules on determining how many significant figures are in a number:
Non-zero digits are always significant.
Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant.
So keeping these rules in mind, there are 4 significant digit.
- One steradian is defined as the angle made by a spherical plane of area 1 square meter at the centre of a sphere of radius 1m.
- One parsec is equal to about 3.26 light years.
- No, since length is fundamental quantity and velocity is the derived quantity and is derived from length and time.
- Diameter of Earth's orbit Radius of Earth's orbit, Let the distance parallax angle be Let the distance of the star be D. Parsec is defined as the distance at which the average radius of the Earth's orbit subtends an angle of 1". We have
Hence, 1 parsec
- Percentage error =
- It is given that angular diameter, = 1920" and distance of the sun from earth, r
=1.496 1011 m. Now let the diameter of sun = d meters
= 9.31 10 -3^ rad Since, d = r Therefore, d =
Now, distance between the Earth and a quasar (using the formula, distance = speed of light × time taken by the light to reach the earth)
m km This is the required distance between earth and a quasar.
- a. Correct
Dimension of y = M^0 L^1 T^0 Dimension of a = M^0 L^1 T^0 Dimension of Dimension of L.H.S = Dimension of R.H.S Hence, the given formula is dimensionally correct. b. Incorrect y = a sin vt Dimension of y = M^0 L^1 T^0 Dimension of a = M^0 L-1T^0 Dimension of vt = But the argument of the trigonometric function must be dimensionless, which is not so in the given case. Hence, the given formula is dimensionally incorrect. c. Incorrect
Dimension of y = M^0 L^1 T^0 Dimension of Dimension of But the argument of the trigonometric function must be dimensionless, which is not so in the given case. Hence, the formula is dimensionally incorrect. d. Correct
Dimension of y = M^0 L^1 T^0 Dimension of a = M^0 L^1 T^0
Dimension of Since the argument of the trigonometric function must be dimensionless (which is true in the given case), the dimensions of y and a are the same. Hence, the given formula is dimensionally correct.
- i. Mean Value of diameter
Dmean = = = 1.3298 = 1.330 cm ii. Absolute Error in different observations are D 1 = Dmean - d 1 = =0.002 cm D 2 = Dmean - d 2 = = 0 cm D 3 = Dmean - d 3 = = + 0.005 cm D 4 = Dmean - d 4 = = 0.004 cm D 5 = Dmean - d 5 = = - 0.004 cm D 6 = Dmean - d 6 = = - 0.006 cm iii. Mean absolute error
= 0.0035 = 0.004 cm iv. Fractional Error = = ±0.003 cm v. Percentage Error = 100 = ±0.003 100% = ±0.3% vi. Diameter of wire = (1.330 ± 0.003) cm or D = 1.330 cm ± 0.3 %
