Question

A football (prolate spheroid) as shown in the gure is placed a height h = 1:5 m

above a horizontal

floor on a fixed pedestal. The football suddenly explodes into two unequal

pieces. Both pieces

fly off horizontally. One piece falls at a distance 1.2 m from the pedestal

to its left. The other piece falls 3.6 m from the pedestal to its right. If the mass of the larger

piece is 300 g, what is the total mass of the ball before it exploded?

Answer 1

the center of mass of the system of mass will be at the same point as the ball was initially.

let the football was initially has X-coordinate as 0 then using the formula

m₁ X₁ = m₂ X₂

m₁ = mass of one piece             m₂ = mass of one piece             

x₁ = 1.2 m                                   x₂ = 3.6 m

m₁ (1.2) = m₂ (3.6)

m₁ = 3 m₂

since m1 is heavier , m₁ = 300 g

so m₂ = 100 g