A cannon shell is firedto hit a target at a horizontal distance d. However , it breaks into two parts of mass ratio 1 : 2 at its height point. The smaller part returns to cannon. The other part (i) will fall at a distance d//2 beyond the target (ii) have eight times the kinetic energy of smaller part (iii) the increase in kinetic energy of system after explosion is 200 % (iv) after explosion , heavier part will take more time as compared to smaller part , to strike the ground

A cannon shell is firedto hit a target at a horizontal distance d. How

1.	A cannon shell is firedto hit a target at a horizontal distance d. However , it breaks into two parts of mass ratio 1 : 2 at its height point. The smaller part returns to cannon. The other part (i) will fall at a distance d//2 beyond the target (ii) have eight times the kinetic energy of smaller part (iii) the increase in kinetic energy of system after explosion is 200 % (iv) after explosion , heavier part will take more time as compared to smaller part , to strike the ground
Answer» `(i) ,(II)` `(i) ,(ii),(iii)` `(i) ,(iii)` all options are correct Solution :`3 md = m xx 0 + 2m x_(0) rArr x_(0) = (3d)/(2)` `x' = x_(0) - d = (3d)/(2) - d = (d)/(2)` (i) is `O.K`. Momentum conservation at the highest point is `3m v COS theta = - mv cos theta + 2mv' rArr v' = 2v cos theta` `(K_(2m))/(K_(m)) = ((1)/(2) ( 2 v cos theta)^(2))/((1)/(2) xx m ( v cos theta)^(2)) = 8` (ii) is `O.K`. `K.E.` before explosion `K_(i) = (1)/(2) xx 3m( v cos theta)^(2) = (3m)/(2) v^(2) cos^(2) theta` `K.E.` after explosion `K_(F) = (1)/(2) m(v cos theta)^(2) + (1)/(2) xx 2m ( 2v cos theta)^(2)` ` = (9m v^(2) cos^(2) theta)/(2)` `((K_(f))/(K_(i)) - 1) xx 100 = 200%` (iii) is `O.K.` Both parts will strike the ground simultaneously , (IV) is wrong.