A ring of radius R is rotating about axis of ring such that angular velocity is given as = 5t. Find acceleration of a point P on rim after 5 sec

Options

A. 5R
B. 25R
C. `sqrt(650)`R
D. None of these

Explanation

To solve the problem of finding the acceleration of a point P on the rim of a rotating ring after 5 seconds, we can follow these steps:

### Step 1: Understand the given data
The angular velocity (ω) of the ring is given as a function of time:
\[ \omega = 5t \]
We need to find the acceleration of a point on the rim after 5 seconds.

### Step 2: Calculate the angular acceleration (α)
Angular acceleration (α) is defined as the rate of change of angular velocity with respect to time. We can calculate it using the formula:
\[ \alpha = \frac{d\omega}{dt} \]
Substituting the expression for ω:
\[ \alpha = \frac{d(5t)}{dt} = 5 \]
Thus, the angular acceleration α is constant and equals 5 rad/s².

### Step 3: Relate angular acceleration to linear acceleration
The linear acceleration (a) of a point on the rim of the ring can be found using the relation:
\[ a = \alpha \cdot R \]
where R is the radius of the ring. Substituting the value of α:
\[ a = 5 \cdot R \]

### Step 4: Evaluate the acceleration after 5 seconds
Since we have determined that the linear acceleration is independent of time (as α is constant), the acceleration of point P on the rim after 5 seconds remains:
\[ a = 5R \]

### Final Answer
The acceleration of point P on the rim after 5 seconds is:
\[ \boxed{5R} \]

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