Question

A particle is thrown at an,angle from the horizontal on earth's surface with an initial velocity u. Then mark the wrong statement assuming zero air resistance:
1. Mechanical energy of the particle is conserved
2. Momentum of the particle is conserved
3. The kinetic energy of the particle is minimum at the highest point
4. The momentum is minimum at the highest point

Answer 1

Correct Answer - Option 2 : Momentum of the particle is conserved

CONCEPT:

Mechanical energy

• The energy possessed by a body due to its position or state of motion is called mechanical energy.
• Mechanical energy is of two types,
  1. Kinetic energy
  2. Potential energy

Kinetic energy

• The energy possessed by a body due to the virtue of its motion is called kinetic energy.

\(\Rightarrow KE=\frac{1}{2}mv^{2}\)

Where KE = kinetic energy, m = mass and v = velocity

Potential energy

• The energy possessed by a body due to its position is called potential energy.

\(\Rightarrow PE=mgh\)

Where PE = increase in potential energy when an object is taken to height h and g = gravitational acceleration

• Linear momentum: It is defined as the product of the mass of an object, m, and its velocity, v. It, is a vector quantity.​

​⇒ P = mv

EXPLANATION:

• When an object is thrown upward and no external force other than the gravitational force is acting on an object then its velocity decreases as the object moves upward and becomes zero when the object is at the maximum height.
• After that, the object starts moving downward and its velocity starts increasing with a downward motion.
• So during the upward motion, the kinetic energy starts converting into potential energy, after that the whole kinetic energy gets converted into potential energy at maximum height, and then again the potential energy starts converting into kinetic energy as the object moves downward, hence the mechanical energy of the particle remains conserved.
• At the highest point, the velocity of the particle is zero so kinetic energy is also zero, hence the kinetic energy is minimum at the highest point.
• At the highest point, the velocity of the particle is zero so the momentum of the particle is also zero, hence the momentum is minimum at the highest point.
• During the whole motion, the velocity of the particle continuously changes, hence the momentum of the particle also changes and it is not conserved.
• Hence, option 2 is correct.