Question

An object of mass $50\text{kg}$ is raised to a height of $10\text{m}$ above the ground. If the object is allowed to free fall. What is kinetic energy, when it is half way down? ($g=10{\text{m/s}}^2$)

• A. $1250\text{J}$
• B. $2500\text{J}$
• C. $3750\text{J}$
• D. $5000\text{J}$

Answer 1

The correct option is B $2500\text{J}$

If the object is allowed to fall freely
Initial velocity $u=0$
Acceleration $a=g$
Applying equation of motion
$v^2=u^2+2as$
$v^2=2\times g\times 5$ [$\because s=5\text{m}$, at half way down]
$v^2=100$
$v=10\text{m/s}$
$\therefore$ kinetic energy $=\frac{1}{2}m{v}^2$
$=\frac{1}{2}\times 50\times 100=2500\text{J}$

Hence option B is the correct answer


Or
From Work energy theorem,

$W=\Delta KE$
here only force acting on system is gravity.

So, work done by gravitational force is equal to change in Kinetic energy.
$W_{grav}=K_f-K_i$
Here $K_i=0$, as body is initially at rest

$W_{grav}=mgs=K_f$

When particle is half way down, $s=5$
$K_f=50\times g\times 5=2500J$