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Figure shows a loopthe loop track of rai...

Figure shows a loopthe loop track of raidus R. A car (without engine) starts from a platform at a distance h above the top of the loop and goes around the loop without falling off the track. Find the minimum value of h for a successful looping. Neglect friction.

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Suppose `upsilon` is speed of the car at the topmost point of the loop.
`:. Mgh=(1)/(2)m upsilon^(2) ` or `m upsilon^(2)=2mgh` …(i)
At the top of the loop, `mg+R=(m upsilon^(2))/(r)=(2mgh)/(r)`
where `R` is the normal reaction.
For `h` to be minum, `R=` minimum `=0,`
`:. (2mgh_(min))/(r)=mg, h_(min)=r//2`
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