A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractive index The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image formed as a function of time for `tlt sqrt((2h)/g)`. Consider only the image by a single refraction.

Answer

A, B

Explanation

At time `tlt(sqrt(2h))/g, u=h-1/2gt^2, mu_1=1`

mu/v+g/u=(mu-1)/R`
`mu/v=(mu-1)/R-1/mu=(mu(mu-1)-R)/(muR)`
`v/mu=(uR)/(u(mu-1)-R)`
`=((h-1/2g^2)R)/((h-1/2gt^2)(mu-1)-R)`
`1/muxx(dv)/(dt)=[R(-gt)[(h-1/2gt^2)(mu-1)-R]]`
`+[R(-gt)(h-1/2gt^2)(mu-1)-R]^2`
`(R(h-1/2gt^2))gt(mu-1)`
`(dv)/(dt)xx1/mu=(gtxxR^2)/([(h-1/2gt^2)(mu-1)-R]^2)`
`(dv)/(dt)=(gtxxR^2)/([(h-1/2gt^2)(mu-1)-R]^2)`
=(mugtR^2)/([(h-1/2gt^2)(mu-1)-R]^2)`