Question

A body of mass $1\text{kg}$ is thrown upwards with a velocity $10\text{m/s}$. It momentarily comes to rest after attaining a height of $4\text{m}$. How much energy is lost due to air friction? ($g=10{\text{m/s}}^2$)

• A. $40\text{J}$
• B. $50\text{J}$
• C. $10\text{J}$
• D. $100\text{J}$

Answer 1

The correct option is C $10\text{J}$

According to work-energy theorem,

Net work done on the body $=$ Change in kinetic energy

So, Sum of Work done by the gravity $W_{\text{gravity}}$ and work done by the air friction $W_{\text{air friction}}$ will be equal to the change in the kinetic energy
$W_{\text{gravity}}+W_{\text{air friction}}=\frac{1}{2}m(v^2-u^2)$ $(W_{\text{gravity}}=-mgh)$
$-1\times 10\times 4+W_{\text{air friction}}=-\frac{1}{2}\times 1\times {10}^2$ [$W_{\text{gravity}}=-mgh;u=0\text{m/s}$]
$W_{\text{air friction}}=-50+40=-10\text{J}$

Hence option C is the correct answer.