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A spherical solid ball of 1 kg mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 radian/s. The kinetic energy of rotation is
  • a)
    4500 J
  • b)
    90 J
  • c)
    910 J
  • d)
    9/20 J
Correct answer is option 'D'. Can you explain this answer?
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A spherical solid ball of 1 kg mass and radius 3 cm is rotating about ...
Calculation of Kinetic Energy of Rotation

Given:

Mass of the ball (m) = 1 kg

Radius of the ball (r) = 3 cm = 0.03 m

Angular velocity (ω) = 50 rad/s


Formula:

The kinetic energy of rotation can be calculated using the formula:

K = (1/2)Iω²

Where,

I = moment of inertia


Calculation:

The moment of inertia of a solid sphere is given by:

I = (2/5)mr²

Where,

m = mass of the sphere

r = radius of the sphere


Substituting the given values in the above equation, we get:

I = (2/5) x 1 x (0.03)²

I = 0.00018 kg.m²


Now, substituting the values of I and ω in the formula for kinetic energy, we get:

K = (1/2) x 0.00018 x (50)²

K = 0.45 J


Hence, the kinetic energy of rotation of the ball is 0.45 J, which is equivalent to option D.
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A spherical solid ball of 1 kg mass and radius 3 cm is rotating about ...
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A spherical solid ball of 1 kg mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 radian/s. The kinetic energy of rotation isa)4500 Jb)90 Jc)910 Jd)9/20 JCorrect answer is option 'D'. Can you explain this answer?
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