An object is projected vertically upwards. Neglecting air resistance, which one of the following statements is correct?

Options

A. According to the principle of conservation of energy, total energy of the object is constant throughout the motion.
B. According to the principle of conservation of momentum, the momentum of the object is constant throughout the motion.
C. The object travels equal distance in equal intervals of time during the ascent and descent.
D. The gravitational potential energy of the object increases uniformly with time during the ascent.

Answer

To solve the question regarding the motion of an object projected vertically upwards, we need to analyze the statements provided and determine which one is correct based on the principles of physics, particularly the conservation of energy and the effects of gravity.

### Step-by-Step Solution:

1. **Understanding the Motion**: When an object is projected vertically upwards, it moves against the force of gravity. As it rises, its speed decreases until it reaches the maximum height, where its speed becomes zero before it starts descending.

2. **Conservation of Energy**: The total mechanical energy (kinetic energy + potential energy) of the object remains constant throughout its motion if we neglect air resistance. This means that as the object rises, its kinetic energy decreases while its potential energy increases, and vice versa when it falls.

3. **Analyzing the Statements**:
- **Statement 1**: "According to the principle of conservation of momentum, the momentum of the object is constant throughout the motion."
- This is **incorrect** because the momentum changes as the velocity of the object changes due to the gravitational force acting on it.

- **Statement 2**: "The object travels equal distance in equal intervals of time during the ascent and descent."
- This is **incorrect** because the object does not travel equal distances in equal time intervals; it travels shorter distances as it ascends due to decreasing velocity and longer distances as it descends due to increasing velocity.

- **Statement 3**: "The gravitational potential energy of the object increases uniformly with time during the ascent."
- This is **incorrect** because the increase in potential energy is not uniform; it depends on the height, which changes non-linearly with time due to the acceleration of gravity.

- **Statement 4**: "The total energy of the object is constant throughout the motion."
- This is **correct** because the total mechanical energy (kinetic + potential) remains constant in the absence of air resistance and external forces.

4. **Conclusion**: The correct statement is that the total energy of the object is constant throughout the motion.

### Final Answer:
The correct statement is: "The total energy of the object is constant throughout the motion."