A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle is :

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answer is C.

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Detailed Solution

Concept- Use the property that net acceleration working on the particle is the sum of tangential acceleration and centripetal acceleration, and with a fixed angular velocity, the tangential acceleration becomes zero, to solve the question. The net acceleration acting on the particle is the sum of the tangential and centripetal accelerations.
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Now suppose the particle moves at a rate of two revolutions per second (Rps) .

The particle's angular speed is now

Now substitute the value we have,

Because the angular velocity is constant, the particle's tangential acceleration is zero, as tangential acceleration is a measure of how quickly a tangential velocity varies.
As a result, the net acceleration acting on the particle is converted to centripetal acceleration.

As previously stated, the centripetal acceleration is equal to the square of the linear velocity (v) divided by the radius.
(R) within the circle,

The linear velocity is the product of the angular velocity and the radius of the circle, as we know.

Now, if we replace this number in equation (1) , we get:

Now, replace the values we've got with the values we've got.

As a result, the particle's net acceleration is

Hence, option 3 is the correct answer.

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