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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 ?

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 ?

Grade:9

1 Answers

Anurag Kishore
37 Points
12 years ago

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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