Question

Radius of a sphere is 100cm at 0 celsius and 100.1cm at 100 celsius. Coefficient of cubical expansion of sphere is

Answer 1

100.1=100(1+a(t2-t1))

100.1=100+100a (t2-t1)

100.1-100=100a (t2-t1)

0.1=100a (t2-t1)

0.1/100=a (t2-t1)

0.001=a (100-0)

0.001/100=a

0.00001=a

Cubical expansion =3×linear expansion

g=3×a

g=3×10^-5

g:-gama

a:-alpha

Answer 2

Answer:

The value of coefficient of cubical expansion of sphere is $3\times10^{-5}/^{\circ}\ C$

Explanation:

Given that,

Radius at 0°C = 100 cm

Radius at 100° C = 100.1 cm

We need to calculate the value of coefficient of cubical expansion

Formula of cubical expansion

$V_{f}=V_{i}(1+\gamma\Delta T)$

Where, V= volume

$\gammma = 3\alpha$

$\Delta T$ =Change in temperature

Put the value into the formula

$\dfrac{4}{3}\pi (100.1)^3=\dfrac{4}{3}\pi (100)^3(1+\gamma\times100)$

$(\dfrac{100.1}{100})^3=1+\gamma\times100$

$1.003=1+\gamma\times100$

$\gamma=\dfrac{0.003}{100}$

$\gamma=3\times10^{-5}/^{\circ}\ C$

Hence, The value of coefficient of cubical expansion of sphere is $3\times10^{-5}/^{\circ}\ C$