Question

A circular tube of mean radius 8 cm and thickness 0.04 cm is
melted up and recast into a solid rod of the same length.
The ratio of the torsional rigidities of the circular tube and
the solid rod is
(a) (8.02)⁴ - (7.98)⁴/(0.8)⁴ (b) (8.02)² - (7.98)²/(8.02)² (c) (0.8)²/(8.02)⁴ - (7.98)⁴ (d) (0.8)²/(8.02)³ - (7.98)²

Answer 1

Explanation:

8 cm and thickness 0.04 cm is melted up and recast into a solid rod of the same length. The ratio of the torsional rigidities of the circular tube and the solid rod is

Initial volume=Final volume

∴π[r

2

2

−r

1

2

]lρ=πr

2

lρ

⇒r

2

=r

2

2

−r

1

2

⇒r

2

=(r

2

+r

1

)(r

2

−r

1

)

⇒r

2

=(8.02+7.98)(8.02−7.98)

⇒r

2

=16×0.04=0.64cm⇒r=0.8cm

∴

C

2

C

1

=

r

4

r

2

4

−r

1

4

=

[0.8]

4

[8.02]

4

−[7.98]

4

December 20, 2019