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EXPLANATION.

A) = Find the change in potential

energy of the mass with angle

=> ∆u = uø - uo = - mgr ( 1 - cosø )

B) = Find the kinetic energy as a function

of a angle.

=> ∆Ke + ∆v = 0

=> ∆ke ( ø ) = mgr ( 1 - cosø)

=> ke ( ø) = mgr ( 1 - cos ø)

C) = Find the radial and tangential

acceleration as a function of angle.

=> (a) Ar = v² / r

=> ½mv² = mgr ( 1 - cos ø)

=> v²/r = 2g ( 1 - cos ø)

Therefore,

=> Ar = 2g ( 1 - cos ø)

(b) = At = mgsinø / m = g sinø

D) = Find the angle at which the mass

flies off the sphere.

=> mgcosø - N = mv²/r

we know that,

=> v²/rg = 2g ( 1 - cos ø) / g

=> cos ø = 2 ( 1 - cos ø)

=> cos ø = 2/3

Note = Also see image

Attachment.