Question

a 5kg bodies collides with another stationary body. after the collision the bodies moves in the same direction with one third of the velocity of the first body. the mass of the second body will be what

Answer 1

Here is the answer .Hope you found it easy.

Answer 2

Answer:

The mass of the second body = 10 kg.

Explanation:

Assumptions:

• $\rm m_1$ = mass of the first body.

• $\rm m_2$ = mass of the second body.

• $\rm u_1$ = initial speed of the first body before collision.

• $\rm u_2$ = initial speed of the second body before collision.

• $\rm v_1$ = final speed of the first body after collision.

• $\rm v_2$ = final speed of the second body after collision.

Given, $\rm m_1 = 5\ kg.$ and since the second body was stationary, therefore, $\rm u_2 = 0\ m/s.$

The initial momentum of the first body before collision, $\rm P_{i1} =m_1u_1 = 5u_1.$

The initial momentum of the second body before collision, $\rm P_{i2} =m_2u_2 = m_2\times 0 = 0.$

The final momentum of the first body after collision, $\rm P_{f1} =m_1v_1 = 5v_1.$

The final momentum of the second body after collision, $\rm P_{f2} =m_2v_2.$

According to the law of conservation of linear momentum,

$\rm P_{1i}+P_{2i}=P_{1f}+P_{2f}\\5u_1+0=5v_1+m_2v_2.$

Given that, after the collision, the bodies moves in the same direction with one third of the velocity of the first body, which means,

$\rm v_1=v_2=\dfrac{u_1}{3}.$

Using these values and the law of conservation of linear momentum,

$\rm 5u_1+0=5\dfrac{u_1}{3}+m_2\dfrac{u_1}{3}\\15u_1=5u_1+m_2u_1\\15=5+m_2\\\Rightarrow m_2 = 10\ kg.$