Question

The size of molecules is smaller than the wavelength of visible light.
The light gets scattered towards the earth.
1
lout Tod uniform area of cross section 'A​

Answer 1

Answer:

Consider a small element of length dx at a distance x from the axis of rotation

Mass of the element, dm=

L

m

dx=μdx

where μ=

L

m

The centripetal force acting on the element is

dT=dmω

2

x=μω

2

xdx

As this force is provided by tension in the rod (due to elasticity), so the tension in therod at a distance x from the axis of rotation will be due to the cetripetal force due to all elements between x=x to x=L

∴T=∫

x

L

μω

2

xdx=

2

μω

2

[L

2

−x

2

]....(i)

Let dl be increase in length of the element. Then

Y=

dl/dx

T/A

dl=

YA

Tdx

=

2YA

μω

2

[L

2

−x

2

]dx [Using (i)]

So the total elongation of the whole rod is

l=∫

0

L

2YA

μω

2

[L

2

−x

2

]dx

=

2YA

μω

2

[L

2

x−

3

x

3

]

0

L

=

3

1

YA

μω

2

L

3

=

3

1

YA

mω

2

L

2