When a torque acting upon a system is zero, which of the following will be constant ?

Options

A. Force
B. Linear impulse
C. Linear momentum
D. Angular momentum

Explanation

To solve the question, we need to analyze the relationship between torque and angular momentum. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the definition of torque
Torque (\(\tau\)) is defined as the rate of change of angular momentum (\(L\)) with respect to time. Mathematically, this is expressed as:
\[ \tau = \frac{dL}{dt} \]
where \(\tau\) is the torque and \(L\) is the angular momentum.

### Step 2: Analyze the condition given in the question
The question states that the torque acting upon the system is zero:
\[ \tau = 0 \]
Substituting this into the torque equation gives:
\[ 0 = \frac{dL}{dt} \]

### Step 3: Interpret the implication of zero torque
If the derivative of angular momentum with respect to time is zero, it implies that angular momentum is not changing with time. This means that angular momentum (\(L\)) is constant:
\[ \frac{dL}{dt} = 0 \implies L = \text{constant} \]

### Step 4: Identify the correct answer
Since we have established that angular momentum remains constant when torque is zero, we can conclude that the correct option from the given choices is:
- Angular momentum

Thus, the answer to the question is that when a torque acting upon a system is zero, the quantity that will remain constant is **angular momentum**.

### Final Answer:
**Angular momentum remains constant when torque is zero.**

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