Question

An iron sphere of mass 10 kg is dropped from a height of 80 cm. If the downward acceleration of the sphere is $10m{s}^{-2}$, calculate the momentum of the sphere when it just strikes the ground

• A. 100 kg m/s
• B. 40 kg m/s
• C. 60 kg m/s
• D. 75 kg m/s

Answer 1

The correct option is B 40 kg m/s

Here, initial velocity of sphere, $u=0$
Distance travelled, $s=80cm=0.8m$
Acceleration of sphere, $a=10m{s}^{-2}$
Final velocity of sphere when it just reaches the ground can be calculated using
$v^2-u^2=2as$
$\therefore v^2-0=2\times 10\times 0.8=16$
or $v=\sqrt{16}=4m{s}^{-1}$.
Momentum of the sphere just before it touches the ground $=mv=10\times 4=40kgm{s}^{-1}$