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1. In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 sec. If the speed of sound in water is 1460 ms-1. What is the distance of enemy submarine?
The speed of sound in water v = 1460 ms-1
Time taken by the pulse for to and fro :
t = T/2 = 80s/2 = 40s
v = d/t
d = v × T/2 = 1460 × 40
= 58400 m or 58.40 km.
Ans: (58.40 km)
2. The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.
Radius of the circle r = 3.12 m
Area of the circle A = ?
A = πr2 = 3.14 × 3.12 × 3.12 = 30.566016
According to the rule of significant fig,
A = 30.6 m2 [Given data has three sig. fig.]
Ans: (30.6 m 2)
3. Assuming that the frequency γ of a vibrating string may depend upon i) applied force (F) ii) length (l) iii) mass per unit length (m), prove that γa using dimensional analysis.
γ ∝ lm Fb mc
γ = K lm Fb mc
K - dimensionless constant of proportionality
a,b,c - powers of l, F, m
Dimensional Formula of F = [MLT-2]
Dimensional Formula of linear density
Applying the principle of homogeneity of dimension
b + c = 0 ....(1)
a + b -c = 0 ….. (2)
4. Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.
Ans: (1.428 × 105 km)
5. The measurement value of length of a simple pendulum is 20 cm known with 2 mm accuracy. The time for 50 oscillations was measured to be 40 s within 1 s resolution. Calculate the percentage accuracy in the determination of acceleration due to gravity ‘g’ from the above measurement.
The errors in both Z & T are least count errors.
1. Why is it convenient to express the distance of stars in terms of light year (or) parsec rather than in km?
The distances of astronomical objects like stars, planets etc from the earth are huge. The distance on the earth are relatively small so it can be measured in km.
For Example :
The distance to be next nearest big galaxy Andromeda is 21,000,000,000,000,000,000 km. i.e. 21 × 1018 km.
This number is so large that it becomes hard to write and to interpret.
So astronomical units like light year, parsec A.U are used for large distances.
2. Show that a screw gauge of pitch 1 mm and 100 divisions is more precise than a vernier caliper with 20 divisions on the sliding scale.
Least count of screw gauge
So screw gauge is more precise than vernier.
3. If humans were to settle on other planets which of the fundamental quantities will be in trouble? Why?
Time will be in trouble. Time becomes irrelevant. Because day and year based on spinning and revolution of the planet. So each planet has its own year length.
Eg. : Uranus and Neptune move too slow.
4. Having all units in atomic standards is more useful. Explain.
All units in atomic standards are more useful because they never change with time.
5. Why dimensional methods are applicable only up to three quantities?
If a quantity depends on more than three factors than dimensional formula cannot be derived. Because on equating the powers of M, L & T on either side of the dimensional equation three equations can be obtained, from which only three unknown dimensions can be calculated.
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