A body is projected from ground obliquely. During downward motion, power delivered by gravity of it

Options

A. Increases
B. Decreases
C. Remains constant
D. First decreases and then becomes constant

Answer

To solve the problem of finding the power delivered by gravity during the downward motion of a body projected obliquely, we can follow these steps:

### Step 1: Understand the Forces Acting on the Body
When a body is projected obliquely, the only force acting on it during its downward motion (after reaching the maximum height) is the gravitational force. This force can be represented as:
\[ F = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

**Hint:** Remember that the gravitational force is constant and acts downward.

### Step 2: Analyze the Motion of the Body
As the body moves downward after reaching its maximum height, its velocity increases due to the acceleration caused by gravity. Initially, at the maximum height, the velocity is zero, and as it falls, the velocity increases.

**Hint:** Consider how the velocity changes from the maximum height to the point just before it hits the ground.

### Step 3: Define Power in Terms of Force and Velocity
Power delivered by a force is defined as the product of the force and the velocity of the object in the direction of the force. Mathematically, it can be expressed as:
\[ P = F \cdot v \]
In this case, since the force is gravity, we can write:
\[ P = mg \cdot v \]
where \( v \) is the velocity of the body during its downward motion.

**Hint:** Remember that power is the rate at which work is done, and it depends on both the force and the velocity.

### Step 4: Determine the Relationship Between Power and Velocity
As the body falls, the velocity \( v \) increases. Therefore, since the force \( F = mg \) is constant, the power \( P \) will also increase as the velocity increases:
\[ P = mg \cdot v \]
As \( v \) increases, \( P \) increases.

**Hint:** Think about how the increasing velocity affects the overall power delivered by gravity.

### Step 5: Conclusion
Thus, during the downward motion of the body, the power delivered by gravity increases as the body gains speed.

**Final Answer:** The power delivered by gravity increases during the downward motion of the body.

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