Question:

A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity $v\, m/s$. If it is to climb the inclined surface then $v$ should be

Updated On: Jul 14, 2022
  • $\geq \sqrt{\frac{10}{7} g h}$
  • $\ge\sqrt{2gh}$
  • $2gh$
  • $\frac{10}{7} g h$
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The Correct Option is A

Solution and Explanation

Kinetic energy is converted to potential energy. From law of conservation of energy, energy can neither be created nor destroyed but it remains conserved. In the given case the sum of kinetic energy of rotation and translation is converted to potential energy.
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Concepts Used:

System of Particles and Rotational Motion

  1. The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
  2. The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
  3. The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.