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

The correct option is 800 J.

Step-by-Step Explanation:

1. Identify the given parameters:
Let $m_1$ be the mass of the first object: $m_1=20\text{kg}$.
Let $u_1$ be the initial velocity of the first mass: $u_1=10\text{m/s}$.
Let $m_2$ be the mass of the second, stationary object: $m_2=5\text{kg}$.
Since the second mass is stationary, its initial velocity $u_2=0\text{m/s}$.

2. Apply the Principle of Conservation of Linear Momentum:
According to the law of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision. Since the two masses stick together after the collision, they form a composite mass of $(m_1+m_2)$ moving with a common final velocity, $v$.

$m_1{u}_1+m_2{u}_2=(m_1+m_2)v$

Substitute the given values into the momentum equation:
$\left(20\right)\left(10\right)+\left(5\right)\left(0\right)=(20+5)v$
$200=25v$
Solve for the common final velocity $v$:
$v=\frac{200}{25}=8\text{m/s}$

3. Calculate the Kinetic Energy of the composite mass:
The kinetic energy ($\mathrm{K.E.}$) of the combined moving system after the collision is given by:
$\mathrm{K.E.}=\frac{1}{2}(m_1+m_2)v^2$

Substitute the total mass and the final common velocity into this formula:
$\mathrm{K.E.}=\frac{1}{2}\left(25\right){\left(8\right)}^2$
$\mathrm{K.E.}=\frac{1}{2}\left(25\right)\left(64\right)$
$\mathrm{K.E.}=25\times 32=800\text{J}$

Thus, the kinetic energy of the composite mass after the collision is 800 J.