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Chapter 14: Q37. (page 385)

A 5.0-m-diameter solid aluminum sphere is launched into space. By how much does its diameter increase? Give your answer in mm.

Short Answer

Expert verified

2.4μm

Step by step solution

01

Given Info

Aluminum sphere

Radius: 5m

Initial Pressure: 1atm

Final pressure: 0

New Radius (radius in space): ?

02

Formula Used

B=∆P∆VV

Where, B = Bulks Modulus

P = Pressure

V = Volume

03

Substituting Values

Let new radius of the sphere(in space) be x.

⇒7×1010=10132543πx3-43π5343πx3⇒7×1010=101325x3x3-125⇒(7x3×1010)-(875×1010)=101325x3⇒(7x3×1010)-101325x3=875×1010⇒x3=875×1010(7×1010)-101325⇒x3=125.0001809⇒x=5.0000024119

And therefore change in radius is x - 5 = 0.0000024m or 2.4μm

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