Conservation of Linear Momentum (11Acd06)

Sheet 02

1. A \(30kg\) shell is flying at \(48ms^{-1}\). When it explodes its one part of \(18kg\) stops, while the remaining part flies off, what will be the velocity of other?
   
   Ans: \(120\frac{m}{s}\).
   
   
2. A bullet of mass \(7g\) is fired into a block of metal weighing \(7kg\). The block is free to move. After the impact , the velocity of bullet and the block is \(0.7ms^{-1}\). What is the initial velocity of the bullet?
   
   Ans: \(700.7\frac{m}{s}\).
   
   
3. A bomb is thrown in a horizontal direction with a velocity of \(50ms^{-1}\). It, explodes into two fragments of masses of \(6kg\) and \(3kg\). The heavier fragments continues to move in the horizontal direction with a velocity of \(80ms^{-1}\). Calculate: The velocity of lighter fragments?
   
   Ans: \(V_{2}=-10\frac{m}{s}\).
   
   
4. A machine gun fires a bullet of mass \(40g\) with a velocity of \(1200ms^{-1}\). The person holding the gun can apply a maximum force of \(144N\) on the gun. What is the maximum number of bullet that can be fired from the gun per second?
   
   Ans: \(3\).
   
   
5. A disc of mass \(10g\) is kept floating horizontally by throwing \(10\) marbles per second against it from below. If the mass of each marbles is \(5g\), then calculate the velocity with which the marbles strikes the disc normally and rebound downward with the same velocity?
   
   Ans: \(0.98\frac{m}{s}\).
   
   
6. A bag of sand of mass \(M\) is hanging from a rope. A bullet of mass \(\frac{M}{x}\) is fired at with a velocity \(v\). The bullet gets imbedded into the sand bag. What is the velocity of the bag after the bullet gets embedded into it?
   
   Ans: \(V=\frac{v}{x+1}\).
   
   
7. A bomb at rest explodes into three pieces of the same mass. The momentum of two parts are, \(-2p\hat{i}\) and \(p\hat{j}\). Find, the magnitude of momentum of \(3^{rd}\) part.
   
   Ans: \(p_{3}=\sqrt{5}p\).
   
   
8. A bomb at rest explodes into three fragments of equal masses. Two fragments fly off at right angle to each other with a velocity of \(9ms^{-1}\) and \(12ms^{-1}\) respectively. Calculate: Speed of \(3^{rd}\) fragment.
   
   Ans: \(15\frac{m}{s}\).
   
   
9. A hammer of mass \(M\) strikes a nail of mass \(m\) with a velocity of \(20ms^{-1}\) into a fixed wall. The nail penetrates into the wall to a depth of \(1cm\). Calculate: Average resistance of the wall to the penetration of the nail?
   
   Ans: \(F=F=\frac{-2M^{2}}{\left(M+m\right)}\times 10^{4}N\).