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A partical moves in a conservation filed...

A partical moves in a conservation filed with no other forces acting on it. At a given instant, the kinetic energy of the particle is 0.5 J and potential energy is `-0.3H.`
STATEMENT 1 The particle must escape the field at same instant of time
STATEMENT 2. The total machanical energy of the particle is positive.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the two statements given regarding the particle moving in a conservative field. ### Step 1: Understand the given information We are given: - Kinetic Energy (KE) = 0.5 J - Potential Energy (PE) = -0.3 J ### Step 2: Calculate the Total Mechanical Energy (TME) The Total Mechanical Energy (TME) of the particle is the sum of its kinetic and potential energy. \[ \text{TME} = \text{KE} + \text{PE} \] Substituting the values we have: \[ \text{TME} = 0.5 \, \text{J} + (-0.3 \, \text{J}) = 0.5 \, \text{J} - 0.3 \, \text{J} = 0.2 \, \text{J} \] ### Step 3: Analyze Statement 2 Statement 2 claims that the total mechanical energy of the particle is positive. From our calculation: \[ \text{TME} = 0.2 \, \text{J} \quad (\text{which is positive}) \] Thus, Statement 2 is **true**. ### Step 4: Analyze Statement 1 Statement 1 claims that the particle must escape the field at the same instant of time. In a conservative field, if the total mechanical energy is positive, the particle has enough energy to escape the potential well. Since we have established that the TME is positive, this implies that the particle can indeed escape. Thus, Statement 1 is also **true**. ### Conclusion Both statements are true based on our analysis: - **Statement 1**: True (the particle must escape the field). - **Statement 2**: True (the total mechanical energy is positive). ### Final Answer Both statements are true. ---
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