A bomb of mass 20 kg initially at rest explodes into three pieces of mass 10 kg, m1 and m2. If the heavier one remains at rest and other move in opposite direction to each other with same speed of 10 m/s. Then find the ratio of m1 to m2.
To solve this problem, we can make use of the law of conservation of momentum. According to this law, the total momentum before the explosion is equal to the total momentum after the explosion.
Before the explosion:
The bomb is initially at rest, so its momentum is zero.
After the explosion:
Let's assume that m1 and m2 are the masses of the two pieces that move in opposite directions with a speed of 10 m/s. The heavier piece (m3) remains at rest.
Now, let's calculate the total momentum before and after the explosion.
Before the explosion:
Initial momentum = 0
After the explosion:
Momentum of m1 = m1 * velocity = m1 * 10 m/s (in the negative direction)
Momentum of m2 = m2 * velocity = m2 * (-10 m/s) (in the positive direction)
Momentum of m3 (heavier piece) = m3 * 0 = 0 (since it remains at rest)
According to the law of conservation of momentum:
Total momentum before explosion = Total momentum after explosion
0 = m1 * 10 m/s + m2 * (-10 m/s) + 0
Simplifying this equation:
0 = 10m1 - 10m2
10m2 = 10m1
Now, we can find the ratio of m1 to m2 by dividing both sides of the equation by 10m2:
m1 = m2
Therefore, the ratio of m1 to m2 is 1:1.
the total momentum must remain at zero
so, since the moving pieces have the same speed, they must have the same mass.