Question

a solid sphere hung at the lower end of a wire is suspended from a fixed point so as to give an elongation of 0.4mm.when the first solid sphere is replaced by another one made of same material but twice the radius, the new elongation is

Answer 1

Answer:

Elongation = 0.4 mm

New material is twice the radius

To find:

The new elongation.

Solution:

By law,

Stress is directly proportional to strain

Stress = Force / 4 π ( radius )^2

Strain = ΔChange in length / Length

Substituting,

We get,

For first sphere,

ρ * radius * gravity / 3 = 0.4 / l

For second sphere,

ρ * 2 * radius * gravity / 3 = 0.4 / l

Dividing,

2 / 1 = Change in length / 0.4

Hence, The new elongation = 0.8 mm

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