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Nature of Physical World and Measurement | Physics

Numerical Problems

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?

Answers:

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.

Answers:

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.

Answers:

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.

Answers:

The errors in both Z & T are least count errors.

Ans: (6%)