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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt ∶ (Kt + Kr) for the sphere is

  1. 7 ∶ 10
  2. 5 ∶ 7
  3. 2 ∶ 5
  4. 10 ∶ 7

Answer (Detailed Solution Below)

Option 2 : 5 ∶ 7
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Detailed Solution

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Concept:

Whenever object is in rolling motion then it possess two types of kinetic energy which are

1. Translational kinetic energy is due to linear motion of an object.

KT = mv2

where m and v is mass and velocity of the object respectively.

2. Rotational kinetic energy due to rotational motion of an object.

KR = I2

where I and  is moment of Inertia and  angular velocity of the object respectively.

Thus, total kinetic energy of the object is

Total K.E. = KT +KR =  mv2  + I2

Calculation:

If object is rolling, then the rotational kinetic energy is-

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