A smooth spehre of radius R is made to translate oin a straight line with a constant acceleration a. A particle kept on the top of the sphere is released rom there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a functon of the angle `theta` it slides.

Explanation

We solve the above problem with respect to the sphere. So apply a pseudo force on the particle. Now from work energy theorem. work done by ma = change in mechanical energy
ma R sin `theta = (k_(f) + u_(f)) - (k_(i) + u_(i))`
maR sin `theta = (1)/(2) mv^(2) - mgR ( 1 - cos theta)`
`rArr " " (1)/(2) mv^(2) = "maR sin " theta + mgr ( 1 - cos theta ) `
`rArr " " v^(2) = 2 R (a "sin" theta + g - g cos theta)`
`rArr " " v = [ 2R ( "a sin " theta + g - g cos theta ]^(1//1)` m/sec