Question

A body of mass 4 kg is falling freely from rest from a height of 30 m from the ground. If the velocity of the body when it is at a height of 10 m from the ground is 10 m/s\(^1\), then the loss of energy due to air resistance on the body is:

• A. \( 400 \, \text{J} \)
• B. \( 600 \, \text{J} \)
• C. \( 300 \, \text{J} \)
• D. \( 100 \, \text{J} \)

Hint:

Use the conservation of mechanical energy to find the total energy at different points and compare the loss of energy due to external factors like air resistance.

Answer 1

The Correct Option is B

Step 1: The total mechanical energy at the initial height (30 m) is given by the sum of kinetic energy and potential energy. Since the body starts from rest, its initial kinetic energy is zero, and its initial potential energy is: \[ PE_{\text{initial}} = mgh = 4 \times 10 \times 30 = 1200 \, \text{J} \] where \( m = 4 \, \text{kg} \), \( g = 10 \, \text{m/s}^2 \), and \( h = 30 \, \text{m} \). 

Step 2: The kinetic energy at the height of 10 m is: \[ KE_{\text{final}} = \frac{1}{2} mv^2 = \frac{1}{2} \times 4 \times 10^2 = 200 \, \text{J} \] where \( v = 10 \, \text{m/s} \).

 Step 3: The potential energy at a height of 10 m is: \[ PE_{\text{final}} = mgh = 4 \times 10 \times 10 = 400 \, \text{J} \] 

Step 4: The total mechanical energy at the height of 10 m is: \[ E_{\text{final}} = KE_{\text{final}} + PE_{\text{final}} = 200 + 400 = 600 \, \text{J} \] 

Step 5: The loss of energy due to air resistance is the difference between the initial energy and the final energy: \[ \text{Energy loss} = PE_{\text{initial}} - E_{\text{final}} = 1200 - 600 = 600 \, \text{J} \] Thus, the loss of energy due to air resistance is \( 600 \, \text{J} \).