AIIMS 2003 Physics Motion with Air Resistance MCQ Question

To analyze the motion of a ball thrown vertically upwards with air resistance, we need to understand the forces acting on the ball and how they influence its speed over time.

Explanation of the Correct Answer (Option D)

When a ball is thrown upwards, two main forces act on it:

1. Gravitational Force (Weight): This force acts downwards and is given by $F_g = mg$, where $m$ is the mass of the ball and $g$ is the acceleration due to gravity (~9.81 m/s²).
2. Air Resistance (Drag Force): This force acts in the opposite direction to the motion of the ball. It increases with the speed of the ball and can be modeled as $F_d = kv^2$, where $k$ is a constant that depends on factors like the shape and surface area of the ball, and $v$ is the speed of the ball.

As the ball is thrown upwards, it decelerates due to the combined effect of gravity and air resistance. Therefore, the speed of the ball decreases until it reaches its maximum height, where its speed becomes zero.

Speed-Time Graph Analysis:

• Initial Phase (Upwards Motion): The speed decreases gradually as the ball rises. The graph shows a downward slope because the speed is decreasing.
• At Maximum Height: The speed reaches zero, and this is the point where the ball stops momentarily before descending.
• Descent Phase: The ball starts to fall back down. Although it accelerates due to gravity, the air resistance acts against the motion, causing the ball to not reach its initial speed when it returns to the original level. Hence, the speed increases, but the increase is less than what it would be without air resistance.

This results in a speed-time graph that shows a gradual decrease to zero at maximum height and then an increase when falling, but at a speed lower than the initial speed when thrown upwards. The overall shape of the graph is concave downwards during the ascent and concave upwards during the descent.

Why Other Options Are Incorrect

• Option A: This might represent a linear decrease (constant deceleration) to zero and then a sudden increase on the way down. This does not account for air resistance, which would cause the descent speed to increase less sharply than depicted here.

• Option B: This could suggest a constant speed during descent, which is completely inaccurate as it ignores both gravity and air resistance. The ball would not maintain a constant speed due to the influence of these forces.

• Option C: This graph could depict an immediate high speed dropping off sharply, which does not accurately represent the gradual effects of air resistance acting on the ball both during ascent and descent.

In summary, the correct speed-time graph (Option D) accurately reflects the gradual decrease in speed during the upward flight and the modified increase in speed during descent due to air resistance, demonstrating the effects of both gravitational and drag forces on the ball's motion.

Key Concepts

• Acceleration due to Gravity: $g \approx 9.81 \, \text{m/s}^2$
• Drag Force: $F_d \propto v^2$
• Net Force: $F_{\text{net}} = F_g - F_d$ during ascent, and $F_{\text{net}} = F_g + F_d$ during descent.

This comprehensive analysis leads us to conclude that the speed-time graph corresponding to the ball thrown upwards with air resistance is best represented by Option D.