I think that answer should be : momentum of 1 will be transferred to 2 and 1 will come at rest as both are having equal masses but here we can say that they will move in same direction

Introduction:
When two spheres of equal masses undergo a glancing elastic collision, their motion after the collision depends on various factors such as the angle of collision, initial velocities, and masses of the spheres. In an elastic collision, both kinetic energy and momentum are conserved.

Explanation:
In the case where one sphere is at rest and the other sphere is moving towards it, the collision can be analyzed using the principle of conservation of momentum and kinetic energy.

Conservation of Momentum:
The total momentum before the collision is equal to the total momentum after the collision. Since one sphere is at rest initially, its momentum is zero. Therefore, the total momentum before the collision is equal to the momentum of the moving sphere, which is given by its mass multiplied by its initial velocity.

Conservation of Kinetic Energy:
In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of a sphere is given by one-half times its mass multiplied by the square of its velocity.

Analysis of the Possible Motions:
Based on the conservation laws, we can consider the following possibilities for the motion of the spheres after the collision:

1. Opposite to one another:
If the moving sphere collides head-on with the sphere at rest, they will move in opposite directions after the collision. This occurs when the angle of collision is 180 degrees.

2. In the same direction:
If the moving sphere collides with the sphere at rest at an angle less than 90 degrees, they will move in the same direction after the collision. The angle between their paths will be less than 90 degrees.

3. At some angle to each other:
If the moving sphere collides with the sphere at rest at an angle between 90 and 180 degrees, they will move at some angle to each other after the collision. The angle between their paths will be greater than 90 degrees but less than 180 degrees.

4. At a right angle to each other:
In a completely glancing collision, where the angle of collision is 90 degrees, the spheres will move at a right angle to each other after the collision. This occurs when the moving sphere strikes the sphere at rest tangentially.

5. Randomly:
If the collision is not perfectly elastic, there may be some random motion after the collision due to energy losses. However, in a perfectly elastic collision, where no energy is lost, the motion will follow the laws of conservation of momentum and kinetic energy.

Conclusion:
In summary, the motion of spheres after a glancing elastic collision depends on the angle of collision. They can move opposite to one another, in the same direction, at some angle to each other, or at a right angle to each other. The specific motion can be determined by analyzing the conservation of momentum and kinetic energy in the collision.