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TV broadcast antennas are the tallest artificial structures on Earth. In 1987, a 72.0 kg physicist placed himself and 400 kg of equipment at the top of one 610 m high antenna to perform gravity experiments. By how much was the antenna compressed, if we consider it to be equivalent to a steel cylinder 0.150 m in radius. a)190 km

b)190 cm

c)190 mm

d)190 μm

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Answer: 190μm

Explanation:

Given the following :

Mass of physicist (m1)= 72kg

Mass of equipment(m2) = 400kg

Height of antenna (L) = 610m

Radius(r) = 0.150

Youngs modulus of steel = 2 × 10^11 Nm^-2

Recall the young's modulus(y) formula :

Y = stress / strain

Stress = force (F) / area(A)

Strain = extension(E) / length (L)

Y = (F/A) ÷ (E/L)

Y = F/A × L/E

Y = FL /AE

Y × AE = FL

E = FL / YA

Area(A) = πr^2

A = π × 0.150^2 = 0.070695m^2

Force (F) = mg

(400 + 72) × 9.8m/s^2 = 4625.6N

THEREFORE :

E = (4625.6 × 610) / (2 × 10^11 × 0.070695)

E = 2821616 / 0.14139 × 10^11

E = 2821616 / 14139000000

E = 0.00019956262819152

E = 0.0001995

E = 1.995 × 10^-4m = 199.5 × 10^-6

Approx E = 190μm

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