A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............
$\frac{1}{2} K a(a-b)$
$\frac{1}{2} K a(a+b)$
$\frac{1}{2} K b(2 a+b)$
$\frac{1}{2} K b(a-b)$
$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
$F = 2x^2 - 3x - 2$. Choose correct option
When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$
$A$ ball is dropped from $a$ height $h$. As it bounces off the floor, its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to $a$ height of most nearly .............. $\mathrm{h}$
Which one of the following statement does not hold good when two balls of masses ${m_1}$ and ${m_2}$ undergo elastic collision