A shell of mass 10 kg flying horizontally with a velocity of 36 kmph e

1.	A shell of mass 10 kg flying horizontally with a velocity of 36 kmph explodes in air into two fragments. The larger fragment has a velocity of 25ms-1 & is directed In the same direction as the initial velocity of the shell. The smaller fragment has a velocity of 12.5 ms-1 in the opposite direction. Find the masses of the fragments.
Answer» Let the mass of larger fragment be m₁ = x Then the mass of smaller fragment is m₂ = 10 – x Initial velocity of larger fragment, u₁= 36kmph = 10 ms^-1 . Final velocity of larger fragment, v₁ = 25ms^-1 . Initial velocity of smaller fragment, u₂ = 10ms^-1 . Final velocity of smaller fragment v₂= – 12.5ms^-1 . According to the law of conservation of momentum, mu = m₁v₁ + m₂v₂ 10 × 10 = x.25 + (10 – x) – 12.5 100 = 25x – 125 + 12.5x 225 = 37.5x ∴ x =\(\frac {225}{37.5}\) = 6Kg ∴ Mass of larger fragment, m₁=. 6kg Mass of smaller fragment m₂ = (10 – x) = 4kg.

A shell of mass 10 kg flying horizontally with a velocity of 36 kmph explodes in air into two fragments. The larger fragment has a velocity of 25ms-1 & is directed In the same direction as the initial velocity of the shell. The smaller fragment has a velocity of 12.5 ms-1 in the opposite direction. Find the masses of the fragments.

Answer»

Let the mass of larger fragment be m₁ = x

Then the mass of smaller fragment is m₂ = 10 – x

Initial velocity of larger fragment,

u₁= 36kmph = 10 ms^-1 .

Final velocity of larger fragment,

v₁ = 25ms^-1 .

Initial velocity of smaller fragment,

u₂ = 10ms^-1 .

Final velocity of smaller fragment

v₂= – 12.5ms^-1 .

According to the law of conservation of momentum,

mu = m₁v₁ + m₂v₂

10 × 10 = x.25 + (10 – x) – 12.5

100 = 25x – 125 + 12.5x

225 = 37.5x

∴ x =\(\frac {225}{37.5}\) = 6Kg

∴ Mass of larger fragment, m₁=. 6kg

Mass of smaller fragment m₂ = (10 – x) = 4kg.