$A$ particle of mass $m$ moving with kinetic energy $E$ collides head-on elastically with another particle of mass $2m$ at rest. After the collision,the kinetic energy of the first particle is:

Explain the special cases of elastic collision in one dimension.

$A$ ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $m/s$.

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. What is the loss in kinetic energy of the colliding body?

$A$ steel sphere of radius $1.2 \ cm$ collides with a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity,then the radius of the second sphere is (in $cm$)

$A$ car of mass $400 \ kg$ is moving with a speed of $72 \ km/h$. It collides with a truck of mass $4000 \ kg$ moving in the same direction with a speed of $9 \ km/h$. After the collision,the car rebounds with a speed of $18 \ km/h$. Find the speed of the truck after the collision in $km/h$.