Question

a bomb of mass 20 kg initially at rest exploded into 3 pieces of mass 10kg M1 and M2 if the heavier mass 1 remains at rest and other moves in opposite direction to each other reach a speed of 10 metre per second then find the ratio of M1 to M2 ?​

Answer 1

Answer:

M1 : M2 = 1 : 1

Step-by-step explanation:

Since

Total mass of bomb = 20 Kg

Mass of first piece = 10 Kg

Mass of second piece = M1 Kg

Mass of third piece = M2 Kg

since by law of conservation of mass

Total mass = sum of masses of all piece

So

      20 Kg = 10 Kg + M1 Kg + M2 Kg

⇒   M1 + M2 = 10 kg

This implies that M1 and M2 are small masses which are to move in opposite directions because big piece has mass 10 kg and sum of M1 and M2 is 10 Kg.So both M1 and M2 is smaller then 10 Kg

NOW

Since when the bomb is explode then equal force act on all direction.

And if mass M1 and M2 gain the speed of equal magnitude (that is 10 m/s) this implies that they are both of same masses

that is

M1 = M2

And using above equation

M1 + M2 = M1 + M1 = 10 Kg

And

2 M1 = 10 Kg

Thus

M1 = 5 Kg

And So

M2 = 5 Kg

And

Ratio of M1 and M2 = M1 : M2 = 5 : 5 = 1 : 1

Thus

M1 : M2 = 1 : 1