Two balls are thrown simultaneously from top of tower in air as shown in the figure.
(i) The acceleration of the center of mass of two balls while in air is equal to `g`.
(ii) The path followed by the center of mass is parabola.
(iii) The path followed by the center of mass will change if one ball after striking the ground comes to rest.

Options

A. `(i),(ii) ,(iii)`
B. `(i),(ii) ,(iv)`
C. `(i),(ii)`
D. all of the above

Answer

C

Explanation

`m_(1) = m_(1) , vec(a)_(1) = -g hat(j) ,m_(2) = 2m , vec(a)_(2) = -g hat(j)`
`vec(a)_(c.m.) = (m_(1) vec(a)_(1) + m_(2) vec(a)_(2))/(m_(1) + m_(2)) = (-m g hat(j))/(3m) = -g hat(j)`
`|vec(a)_(c.m.)| = g , (i) is O.K`.
`(m + 2m) vec(u)_(c.m.) = (mu_(1) cos alpha + 2mu_(2) cos beta) hat(i)`
`+ (mu_(1) sin alpha - 2m u_(2) sin beta) hat(j)`
`= u_(x) hat(i) + u_(y) hat(j)`
`vec(x)_(c.m.) = u_(x) hat(i) t , vec(y)_(c.m.) = u_(y) t hat(j) - (1)/(2) gt^(2) hat(j)`
Trajectory `y = (u_(y))/(u_(x)) x - (1)/(2) (gx^(2))/(u_(x)^(2))`, parabola