Question

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is _______ N.}

• A. 1980
• B. 2020
• C. 2000
• D. 1000

Answer 1

The Correct Option is C

Step 1: Using the work-energy principle.
According to the work-energy theorem, the work done by the force is equal to the change in kinetic energy. The potential energy lost by the ball is converted into work done to stop the ball. The potential energy lost by the ball is given by: \[ PE = mgh \] where \( m = 2 \, \text{kg} \), \( g = 10 \, \text{m/s}^2 \), and \( h = 10 \, \text{m} \). Therefore: \[ PE = 2 \times 10 \times 10 = 200 \, \text{J} \]
Step 2: Calculating the work done by the force.
The work done by the average force is \( W = F \times d \), where \( d = 0.1 \, \text{m} \) (the distance penetrated into the sand). The work done to stop the ball is equal to the potential energy lost, so: \[ F \times 0.1 = 200 \quad \Rightarrow \quad F = \frac{200}{0.1} = 2000 \, \text{N} \]
Step 3: Conclusion.
The average force exerted by the sand on the ball is 2000 N.
Final Answer: (C) 2000