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

Approved