Question

A particle is describing uniform circular motion on a circle of radius 5 cm with speed of 10cm/s,it's centripetal acceleration will be
A)50cm s^-2
B)2cm s^-2
C)2.5cm s^-2
D)20cm s^-2​

Answer 1

Step-by-step explanation:

Answer :-

Centripetal acceleration of the particle will be 20 cm/s² [Option.D]

Explanation :-

We have :-

→ Radius of the circle = 5 cm

→ Speed of the particle = 10 cm/s

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We know that, when a particle is undergoing uniform circular motion, then it's acceleration is given by :-

a꜀ = v²/r

Where :-

• a꜀ is the centripetal acceleration.

• v is speed of the particle.

• r is radius of the circle.

Substituting values, we get :-

⇒ a꜀ = v²/r

⇒ a꜀ = (10)²/5

⇒ a꜀ = 100/5

⇒ a꜀ = 20 cm/s²

Answer 2

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The distance covered in completing the circle 2πr=2π×10cm. 

The linear speed is v=2πr/t=4s2π×10cm=5πcm/s

The acceleration is a=rv2=10cm(5πcm/s)2=2.5π2cm/s2.

Hence, the magnitude of its acceleration is =2.5π2cm/s2.