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A particle of mass m is released from po...

A particle of mass m is released from point A as shown in the gigure. Would it loop the loop if H=4r? What is the force on the circular track when it is at point (a) B, (b) C?

Text Solution

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Hint : Let speed at the lowest point B by `v_(B)`
Total energy at A = Total energy at B
`0+mgH+(1)/(2)mv_(B)^(2)`
`v_(B)=sqrt(gH)=sqrt(8gr)`
Let `N_(1)` be the force exerted by the track at B.
`N_(1)=mg+(mv_(B)^(2))/(r )`
If `v_(C)` is velocity at C
`v_(C)^(2)=v_(B)^(2)-4gr`
`N_(2)` is force exerted by the track at C.
`N_(2)=(mv_(C)^(2))/(r )-mg`
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