Uranus has a mass of 8.68 1025 kg and a radius of 2.56 107 m. Assume it is a uniform solid sphere. The distance of Uranus from the Sun is 2.87 1012 m. (Assume Uranus completes a single rotation in 17.3 hours and orbits the Sun once every 3.08 104 Earth days.)

(a) What is the rotational kinetic energy of Uranus on its axis?

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(b) What is the rotational kinetic energy of Uranus in its orbit around the Sun?

J

Answer

Given,

Mass of the Uranus, M = 8.68 x 10²⁵ Kg

Radius of Uranus, R = 2.56 x 10⁷ m

Distance of Uranus, D = 2.87 x 10¹² days

a) Rotational Kinetic energy of the Uranus

moment of inertia of the Uranus

         I = 22.75 x 10³⁹ kg.m²

  Angular speed

     \

 Rotational Kinetic energy

b) Rotational Kinetic energy of Uranus in its orbit around sun

moment of inertia of the Uranus

      I = 7.15 x 10⁵⁰ kg.m²

Angular speed

     \

 Rotational Kinetic energy

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

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step-by-step explanation: