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.