A body is revolving with a uniform speed v in a circle of radiusr . The tangential acceleration is

Options

A. `(v)/(r)`
B. `(v^(2))/(r)`
C. Zero
D. `(v)/(r^(2))`

Answer

To solve the problem of finding the tangential acceleration of a body revolving with uniform speed \( v \) in a circle of radius \( r \), we can follow these steps:

### Step 1: Understand the Concept of Tangential Acceleration
Tangential acceleration is defined as the rate of change of the speed of an object moving along a circular path. It is given by the formula:
\[ a_t = \frac{dv}{dt} \]
where \( dv \) is the change in velocity and \( dt \) is the change in time.

### Step 2: Analyze the Given Conditions
In this problem, the body is revolving with a uniform speed \( v \). This means that the speed of the body does not change over time. Therefore, the change in speed \( dv \) is equal to 0.

### Step 3: Substitute the Values into the Formula
Since the speed is constant:
\[ dv = 0 \]
Now, substituting this into the formula for tangential acceleration:
\[ a_t = \frac{dv}{dt} = \frac{0}{dt} = 0 \]

### Step 4: Conclusion
Thus, the tangential acceleration \( a_t \) of the body revolving with uniform speed \( v \) in a circle of radius \( r \) is:
\[ a_t = 0 \]

### Final Answer
The tangential acceleration is \( 0 \).

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