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Question

A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal.


A

g

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B

2g

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C

3g

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D

6g

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Solution

The correct option is C

3g


Step1: Given data

The object at the top of the vertical circle has a speed equal to critical speed.

Step2: Formula used

The critical speed at the top of a vertical circle, vc=gl[whereg=accelerationduetogravity,l=radiusoftheverticalcircle]

At a point in a horizontal circle, when the string becomes horizontal, the speed of the object,

v2=u2+2gh[wherev=finalspeed,u=initialspeed,g=acceleartionduetogravity,h=changeinheight]

Step3: Calculating the final speed.

According to the given data, the speed of the object at the topmost point =gl

This will act as the initial speed for when the string becomes horizontal i.e. u=gl

Therefore the speed of the object at this point will be

v2=(gl)2+2gh

The change in height of the object from the initial point is equal to,

v2=gl+2gl=3gl
Step4: Calculating centripetal acceleration

ac=v2lac=3gllac=3g

The centripetal acceleration when the string becomes horizontal is 3g.

Hence, option C is the correct answer.


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