Question

if earth were to shrink to half its present diameter with a change in mass half of the initial value then the duration of the day will be​

Answer 1

Given,

Diameter and mass become half.

To find,

The length of the day.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

If the diameter shrinks to half, then it's obvious that the radius will also shrink to half.

Let,

Radius before contraction = R1

Radius after contraction = R2

Mass before contraction = M1

Mass after contraction = M2

Moment of inertia before contraction = I1

Moment of inertia after contraction = I2

Angular velocity before contraction = ω1

Angular velocity after contraction = ω2

Length of day before contraction = T1 = 24 hours

Length of day after contraction = T2

According to the data mentioned in the question,

M2 = M1/2

R2 = R1/2

Now,

I1 × ω1 = I2 × ω2

⅖ × M1 × R1² × 2π/T1 = ⅖ × M2 × R2² × 2π/T2

⅖ × M1 × R1² × 2π/24 = ⅖ × M1/2 × (R1/2)² × 2π/T2

⅖ × M1/2 × (R1/2)² × 2π/T2 = ⅖ × M1 × R1² × 2π/24

2π/T2 = ⅖ × M1 × R1² × 2π/24 × ⁵/₂ × 2/M1 × 4/R1²

2π/T2 = 2π/24 × 2 × 4

2π/T2 = 2π/3

2π × T2 = 3 × 2π

T2 = 3 × 2π/2π

T2 = 3

Hence, length of the day will be 3 hours.

Answer 2

Answer:

3 hr

Explanation:

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