Given:
rod of circular cross section is subjected to uniaxial tension.
Length, L=1500 mm
radius, r = 10 mm
E=2*10^5 N/mm^2
Force, F=20 kN = 20,000 N
[note: newton (unit) in abbreviation is written in upper case, as in N ]
From given above, area of cross section = π r^2 = 100 π =314 mm^2
(i) Stress,
σ
=force/area
= 20000 N / 314 mm^2
= 6366.2 N/mm^2
= 6370 N/mm^2 (to 3 significant figures)
(ii) Strain
ε
= ratio of extension / original length
= σ / E
= 6366.2 /(2*10^5)
= 0.03183
= 0.0318 (to three significant figures)
(iii) elongation
= ε * L
= 0.03183*1500 mm
= 47.746 mm
= 47.7 mm (to three significant figures)
I'll just find out the path difference between the waves at the starting point. At infinity, the path difference will be zero because the observer will be infinitely far away from both. As the observer goes farther, the path difference keeps reducing till it reaches zero as the observer reaches infinity.
<span>Path difference at starting point = Distance from lower speaker - Distance from upper speaker = √((3)² + (2.5)²) - 2.5 = 1.405 m </span>
<span>Now to find wavelength. </span>
<span>Speed of sound in air at 20 degrees C = 343 m/s </span>
<span>Wavelength = 343 / 686 = 0.5 m </span>
<span>Destructive interference occurs when path difference = (2n + 1)λ/2 where n is an integer. </span>
<span>Maximum n possible can be found by, </span>
<span>(2n + 1)λ/2 < 1.405 </span>
<span>(2n + 1) < (1.4)(2) / (0.5) </span>
<span>2n < 5.6 - 1 </span>
<span>2n < 4.6 </span>
<span>n < 2.3 </span>
<span>So, we have 3 values of n, 0, 1 and 2. </span>
<span>Path differences are, λ/2, 3λ/2 and 5λ/2 which have values 0.25 m , 0.75 m and 1.25 m </span>
<span>But the question asks for distance from starting point. (sheesh!!) </span>
<span>Lets say the observer walked x distance. </span>
<span>Path difference = √((3)² + (2.5 + x)²) - (2.5 + x) </span>
<span>Equate this expression to the values obtained above to get the different values of x. </span>
Answer:
The illumination on the book before the lamp is moved is 9 times the illumination after the lamp is moved.
Explanation:
The distance of the book before the lamp is moved,
The distance of the book after the lamp is moved,
Illumination can be given by the formula,
Illumination before the lamp is moved,
Illumination after the lamp is moved,
The illumination on the book before the lamp is moved is 9 times the illumination after the lamp is moved.
Answer:
Maximum height, h(t) = 95 meters
Explanation:
A ball travels on a parabolic path in which the height (in feet) is given by :
.............(1)
Where
t is the time after launch
We need to find the maximum height of the ball in feet. For maximum height,
t = 2
Put the value of t in equation (1) as :
h(t) = 95 meters
So, the maximum height of the ball is 95 meters. Hence, this is the required solution.
Answer:
The required radial distance from the center of the toroid is -
<u>r = 4.34 cm</u>
Explanation:
We know that magnetic field inside a solenoid is given by -
B = μni
where 'μ' is the magnetic permeability , 'n' is the number of turns per unit length , 'i' is the current passing through solenoid.
given n = 550 turns/meter
We know that magnetic field inside a toroid is -
B = μ××i [Current is same in both the devices] , where 'N' is the total number of turns in the toroid and 'r' is the radial distance from the center of the toroid.
Given N = 150.
Equating the two magnetic fields , we get -
μni = μ××i
∴
Substituting the values we get -
r = 0.0434 m = 4.34 cm