Question

A body of mass 2 kg moving with a velocity of 3ms⁻¹ collides head on with a body of mass 1 kg moving with a velocity of 4 ms⁻¹ in opposite direction. After collision the two bodies stick together and move with a common velocity.

a. 2/3 ms⁻¹
b. ¾ ms⁻¹
c. ¼ ms⁻¹
d. 1/3 ms⁻¹

Answer 1

The common velocity of the two bodies after the collision is 2/3 ms⁻¹.

Step-by-step explanation:

In this collision problem, we can use the principle of conservation of momentum to find the common velocity of the two bodies after the collision. The momentum of an object is given by the product of its mass and velocity.

Before the collision, the total momentum of the system is the sum of the momenta of the two bodies:

(2kg)(3ms⁻¹) + (1kg)(-4ms⁻¹) = 6kgms⁻¹ - 4kgms⁻¹ = 2kgms⁻¹.

After the collision, the two bodies stick together and move with a common velocity. Let's call this velocity v. The total momentum of the system after the collision is:

(2kg + 1kg)(v) = 3kgv.

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:

2kgms⁻¹ = 3kgv.

Simplifying this equation, we find that the common velocity v after the collision is 2/3 ms⁻¹, which is option a.