Question

A metal rod of mass m and lenth l is rotating with w about an axis passing through o and normal to its length potential difference is bwl^2/6

Answer 1

The change in angular velocity is proportional to ω.

Explanation:

Correct statement:

A uniform metal rod of length 'L' and mass 'M' is rotating about an axis passing through one of the ends perpendiculars to the rod with angular speed 'ω' . If the temperature increases by  t ° C  then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod  = α )

Solution:

The moment of inertia of a rod "I"  =  1 / 3 M L^ 2

• As the temperature increases, the length of the rod also increases.

Thus new length of the rod   L f =L ( 1 + α t )

New moment of inertia of rod = If = ML^3f / 3 = 1/3 ML^2 (1 + α t )^2

Let angular momentum decreases by Δ ω.

According to the principle of conservation of momentum.

Iω = If (ω - Δ ω)

Δ ω =  If - I / If . ω

Δ ω α ω

Thus the change in angular velocity is proportional to ω.

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