Adjustment & Defence Mechanisms
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Under Mechanics, considering the principles of force, motion, and energy, consider the following statements:
- 1. When an object moves on a circular path with uniform speed, the centripetal force acting on it is directed towards the center of the circle traversed by the object, but the work done by this force on the object is zero because the direction of displacement is always perpendicular to the centripetal force.
- 2. In the case of an elastic collision, not only linear momentum is conserved, but total kinetic energy is also completely conserved, and the value of the coefficient of restitution (e) used in it is exactly zero.
- 3. The moment of inertia of an object depends only on its mass, and changing the position of the axis of rotation does not cause any change in the value of the moment of inertia of the object.
- 4. The total energy of a particle performing Simple Harmonic Motion keeps changing continuously with its displacement, and when the particle is at its mean position, its potential energy is maximum and kinetic energy is minimum.
Which of the above statements are completely true?
✓ Correct! Well done.
✗ Not quite — the correct answer is highlighted above.
Detailed Explanation
Statement 1 is true because when an object performs uniform circular motion, the centripetal force acts along the radius towards the center and displacement is always along the tangent, making the angle between force and displacement 90°; since $W = F s \cos(90^\circ)$, the work done is zero. Statement 2 is false because for a perfectly elastic collision, the value of the coefficient of restitution ($e$) is 1, not zero (zero is for a perfectly inelastic collision). Statement 3 is false because the moment of inertia depends on the mass of the object as well as the square of the distance of particles from the axis of rotation ($mr^2$), so it changes when the axis changes. Statement 4 is false because in simple harmonic motion, the velocity is maximum at the mean position, so kinetic energy is maximum and potential energy is zero.
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