A small spherical ball of mass m is projected from lowest point (point P) in the space between two fixed, concentric spheres A and B (see figure). The smaller sphere A has a radius R and the space between the two spheres has a width d. The ball has a diameter very slightly less than d. All surfaces are frictionless. Speed of ball at lowest point is v. NA and NB represent magnitudes of the normal reaction force on the ball exerted by the spheres A and B respectively. Match the value of v given in column–I with corresponding results in column–II.

Options

A. a. `{:("Column-I",,"Column-II"),((A)v=sqrt(gR),,(p)"maximum value of " N_(A)=0):}`
B. b. `{:("Column-I",,"Column-II"),((B) v=sqrt(2gR),,(q)"minimum value of " N_(B)=0):}`
C. c. `{:("Column-I",,"Column-II"),((C) v=sqrt(3gR),,(r) "maximum value of "N_(B)=6 mg):}`
D. d. `{:("Column-I",,"Column-II"),((D) v=sqrt(5gR),,(s)"maximum value of " N_(B)=4 mg),(,,(t) "maximum value of " N_(B)=2 mg):}`

Explanation

Ball only loose contact with surface B when v is in range `sqrt(2Rg) lt v lt sqrt(5 Rg)` so for A,B,D maximum value of `N_(A)` is zero for option C ball lose contact with surface V at some point. Maximum value of `N_(B)` is lowest point and given
`N=mg+(mv^(2))/R`