Question

11. A body of mass 5kg is moving towards north with a velocity of 4m/s. Another body of
mass 3kg is moving towards south with a velocity 2m/s. at a particular time two bodies
collided and became a single body. At what velocity and at which direction the combined
body will move?

Answer 1

$\displaystyle\large\boxed {\sf {\dfrac {7}{4}\ m\ s^{-1}\ towards\ North}}$

Given,

• $\displaystyle\sf {m_1=5\ kg}$

• $\displaystyle\sf {u_1=(4\ \hat n)\ m\ s^{-1}\quad (Say)}$

Then,

• $\displaystyle\sf {m_2=3\ kg}$

• $\displaystyle\sf {u_2=(-2\ \hat n)\ m\ s^{-1}}$

Let the velocity attained by the combined body after collision be $\displaystyle\sf {v.}$

Assuming no mass loss is occurred during collision.

Then, by the law of conservation of linear momentum,

$\displaystyle\longrightarrow\sf {m_1u_1+m_2u_2=(m_1+m_2)v}$

$\displaystyle\longrightarrow\sf {5(4\ \hat n)+3(-2\ \hat n)=(5+3)v}$

$\displaystyle\longrightarrow\sf {20\ \hat n-6\ \hat n=8v}$

$\displaystyle\longrightarrow\sf {14\ \hat n=8v}$

$\displaystyle\longrightarrow\sf {\underline {\underline {v=\left (\dfrac {7}{4}\ \hat n\right)\ m\ s^{-1}}}}$

Therefore, the combined body will move with a velocity of $\displaystyle\sf {\underline {\underline {\dfrac {7}{4}\ m\ s^{-1}\ towards\ North.}}}$