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Q.

A disc is at rest at the top of a rough inclined plane. It rolls without slipping. At the bottom of inclined plane there is a smooth vertical groove of radius ‘R’. In order to loop the groove. the minimum height of incline required is

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a

5R/2

b

7R/5

c

9R/4

d

15R/4

answer is A.

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Detailed Solution

Question Image

According to conservation of energy :
∆PE = ∆KE
mgh=12mv21+K2R2

For disc, K2R2=12

Minimum linear velocity required to loop the circle is

v = 5gR

⇒h=12g5gR21+12=15R4

 

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