(A) : If body or a system has neither translational nor rotational motion then it is in complete mechanical equilibrium.
(R ) : A body or system is said to be in mechanical equilibrium when net force and net torque acting on the body are zero.

Options

A. Both (A) and (R ) are true and (R ) is the correct explanation of (A)
B. Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
C. (A) is true but (R ) is false
D. Both (A) and (R ) are false

Answer

To analyze the given assertion and reason, we can break down the solution into the following steps:

### Step 1: Understanding Mechanical Equilibrium
Mechanical equilibrium occurs when a body or system experiences no net external forces or torques. This means that:
- The sum of all forces acting on the body is zero (translational equilibrium).
- The sum of all torques acting on the body is zero (rotational equilibrium).

### Step 2: Analyzing the Assertion
The assertion states that if a body or system has neither translational nor rotational motion, then it is in complete mechanical equilibrium.
- If there is no translational motion, it implies that the net external force acting on the body is zero.
- If there is no rotational motion, it implies that the net torque acting on the body is zero.

### Step 3: Analyzing the Reason
The reason provided states that a body or system is in mechanical equilibrium when the net force and net torque acting on the body are zero.
- This aligns with our understanding of mechanical equilibrium, confirming that both conditions (net force = 0 and net torque = 0) must be satisfied.

### Step 4: Conclusion
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we can conclude that:
- Both the assertion and the reason are true.
- The reason is the correct explanation for the assertion.

### Final Answer
Thus, the correct option is that both the assertion and reason are true, and the reason is the correct explanation for the assertion.

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