Question

A mass of $20kg$ moving with a speed of $10m{s}^{-1}$ collides with another stationary mass of $5kg$. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be

• A. $600J$
• B. $800J$
• C. $1000J$
• D. $1200J$

Answer 1

The correct option is B

$800J$

Step 1: Given data

Mass of moving body is $m_1=20kg$

Velocity of moving mass $v_1=10m{s}^{-1}$

Mass of stationary body $m_2=5kg$

Velocity of stationary mass $v_2=0m{s}^{-1}$

Step 2: Finding the velocity of combined mass

After collision the two masses stick together, $m=m_1+m_2=20+5=25kg$ and considering its velocity will be $vm{s}^{-1}$

Applying Conservation of momentum,

$$\begin{gathered} m_1\times v_1+m_2\times v_2=m\times v \\ 20\times 10+5\times 0=25\times v \\ v=\frac{200}{25} \\ v=8m{s}^{-1} \end{gathered}$$

Step 3: Finding the kinetic energy of composite mass

$Kineticenergyofcompositemass=\frac{1}{2}m{v}^2$

$$\begin{gathered} =\frac{1}{2}\times 25\times {\left(8\right)}^2 \\ =800J \end{gathered}$$

Thus, the kinetic energy of the composite mass will be$800J$

Hence, option (b) is correct.