Final answer:
Using the principle of conservation of energy, the velocity of the bob at its mean position is calculated by equating the potential energy at the highest point to the kinetic energy at the mean position. After solving the equation, the velocity is found to be approximately 1.4 m/s, which is option (d).
Step-by-step explanation:
The motion of a simple pendulum can be understood using conservation of energy principles. When the pendulum reaches the mean position (the lowest point), all the potential energy that the bob had at the highest point (10 cm above the mean position) has been converted into kinetic energy. To find the velocity of the bob at the mean position, we can use the following equation, which relates gravitational potential energy (GPE) to kinetic energy (KE):
GPE = KE
mgh = ½ mv²
where:
- m is the mass of the bob (cancels out on both sides)
- g is the acceleration due to gravity (9.8 m/s²)
- h is the height (0.10 m)
- v is the velocity at the mean position we want to find
Cancelling the mass from both sides and solving for v gives:
v = √(2gh)
v = √(2 × 9.8 m/s² × 0.10 m)
v = √(1.96 m²/s²)
v ≈ 1.4 m/s
Therefore, the velocity of the bob of a simple pendulum at its mean position, given that it can rise to a vertical height of 10 cm, is approximately 1.4 m/s, which corresponds to option (d).