Q63 of 119 Page 159

A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head-on, the bodies go at right angle to each other after the collision.

As it is not a head on collision, the two bodies move in different dimensions.


Initial velocity of 1st body is u1 and 2nd body is u2=0 (as it is in rest).


Let v1 and v2 are the velocities of the bodies after collision.


Since the collision is elastic


According to law of conservation of momentum (in x direction)



________ (1)


Putting law of conservation of momentum in y direction



_________ (2)


By law of conservation of energy




__________ (3)


Squaring equation (1)




Equating the above equation with equation (3)




From equation (2)








So, it is proven that the collision is not head-on, the bodies go at right angle to each other after the collision.


More from this chapter

All 119 →
60

A block of mass m is placed on triangular block of mass M, which in turn is placed on a horizontal surface as shown in figure (9-E21). Assuming frictionless surfaces find the velocity of the triangular block when the smaller block reaches the bottom end.


 61

Figure (9-E22) shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed u and the system is left to itself. Assume that all the surfaces are frictionless. (a) Find the speed of the larger block when the smaller block is sliding on the vertical part. (b) Find the speed of the smaller mass when it breaks off the larger mass at height h. (c) Find the maximum height (from the ground) that the smaller mass ascends. (d) Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.


 62

A small block of super dense material has a mass of 3 × 1024 kg. It is situated at a height h (much smaller than the earth’s radius) from where it falls on the earth’s surface. Find its speed when its height from the earth’s surface has reduced to h/2. The mass of the earth is 6 × 1024 kg.

 64

A small particle travelling with a velocity υ collides elastically with a spherical body of equal mass and of radius r initially kept at rest. The centre of this spherical body is located a distance ρ(< r) away from the direction of motion of the particle (figure
9-E23). Find the final velocities of the two particles.


[Hint: The force acts along the normal to the sphere through the contact. Treat the collision as one-dimensional for this direction. In the tangential direction no force acts and the velocities do not change].