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A PARTICLE SLIDES ON THE SURFACE OF A FIXED SMOOTH SPHERE STARTING FROM THE TOP MOST POINT . FIND THE ANGLE ROTATED BY THE RADIUS THROUGH THE PARTICLE , WWHEN IT LEAVES CONTACT WITH THE SPHERE ?
Hello,
I am giving you the hint
Let the particle leave contact at an angle @ from vertical
Use two equations
1. Energy conservation between top and point of leaving contact
mgR(1-cos @) = 1/2 mv2 ------------------------- (1)
2.Also see that at the time of leaving Normal force = 0
So
N + mg cos@ = mv2/R but N = 0 as stated above,
so mg cos@= mv2/R ----------------- (2)
where R is radius of sphere and v is velocity of particle at the instant.
From above two equation you can find v and @
Thanks
Anurag
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