Identify, which of th following energies can be positive (or zero) only ?

Options

A. a)Kinetic energy
B. b)Potential energy
C. c)Mechanical energy
D. d)Both kinetic and mechanical energy

Answer

To solve the question "Identify which of the following energies can be positive (or zero) only," we will analyze each option step by step.

### Step 1: Analyze Kinetic Energy
- **Formula**: The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} mv^2 \]
- **Variables**:
- \( m \) (mass) is always positive since mass cannot be negative.
- \( v \) (velocity) can be positive, zero, or negative. However, when we square the velocity (\( v^2 \)), it will always be non-negative (either positive or zero).
- **Conclusion**: Therefore, kinetic energy can only be positive or zero. It cannot be negative.

### Step 2: Analyze Potential Energy
- **Formula**: The formula for potential energy (PE) is:
\[ PE = mgh \]
- **Variables**:
- \( m \) (mass) is always positive.
- \( g \) (acceleration due to gravity) is always positive.
- \( h \) (height) can be positive, negative, or zero.
- **Conclusion**: Since height can take negative values, potential energy can also be negative. Thus, potential energy can be positive, negative, or zero.

### Step 3: Analyze Mechanical Energy
- **Definition**: Mechanical energy (ME) is the sum of kinetic energy and potential energy:
\[ ME = KE + PE \]
- **Conclusion**: Since kinetic energy can only be positive or zero, and potential energy can be positive, negative, or zero, mechanical energy can take any value (positive, negative, or zero). Thus, mechanical energy is not restricted to being positive or zero.

### Step 4: Analyze Both Kinetic and Mechanical Energy
- **Conclusion**: Since kinetic energy can only be positive or zero, and mechanical energy can be positive, negative, or zero, the option stating "both kinetic and mechanical energy" is also not correct in terms of being positive or zero only.

### Final Conclusion
From the analysis:
- **Kinetic Energy** is the only energy that can be positive or zero only.
- **Potential Energy** can be negative, zero, or positive.
- **Mechanical Energy** can also be negative, zero, or positive.
- **Both Kinetic and Mechanical Energy** cannot be restricted to positive or zero only.

Thus, the correct answer is **Option A: Kinetic Energy**.

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