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An iron sphere of mass 10 kg has the same diameter as an aluminium sphere of mass 3.5 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same:
- a)Acceleration
- b)Potential energy
- c)Kinetic energy
Correct answer is option 'A'. Can you explain this answer?
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An iron sphere of mass 10 kg has the same diameter as an aluminium sph...
a) Acceleration
Most Upvoted Answer
An iron sphere of mass 10 kg has the same diameter as an aluminium sph...
They will have same acceleration because acceleration due to gravity is irrespective of mass..it acts equally on any object or particle...
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An iron sphere of mass 10 kg has the same diameter as an aluminium sph...
Understanding the Scenario
When both the iron and aluminium spheres are dropped from the same height, they experience the same conditions of free fall due to gravity.
Key Points about Free Fall
- Acceleration due to Gravity:
- Both spheres accelerate towards the ground at the same rate, which is approximately 9.81 m/s² (the acceleration due to gravity).
- This is independent of their masses, meaning that regardless of whether an object is heavy or light, in a vacuum (without air resistance), they fall at the same rate.
Potential Energy Comparison
- Potential Energy:
- Potential energy (PE) is calculated using the formula PE = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is height above the ground.
- Since the masses of the spheres are different, their potential energies at 10 m will also be different. Therefore, they do not have the same potential energy.
Kinetic Energy Comparison
- Kinetic Energy:
- Kinetic energy (KE) is given by the formula KE = 1/2 mv², where 'm' is mass and 'v' is velocity.
- As both spheres fall, they will reach different velocities by the time they are 10 m above the ground, again leading to different kinetic energies.
Conclusion
Thus, while the two spheres have the same acceleration due to gravity, their potential and kinetic energies differ due to their varying masses. Therefore, the correct answer that they have in common when they are 10 m above the ground is option 'A' - they have the same acceleration.
When both the iron and aluminium spheres are dropped from the same height, they experience the same conditions of free fall due to gravity.
Key Points about Free Fall
- Acceleration due to Gravity:
- Both spheres accelerate towards the ground at the same rate, which is approximately 9.81 m/s² (the acceleration due to gravity).
- This is independent of their masses, meaning that regardless of whether an object is heavy or light, in a vacuum (without air resistance), they fall at the same rate.
Potential Energy Comparison
- Potential Energy:
- Potential energy (PE) is calculated using the formula PE = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is height above the ground.
- Since the masses of the spheres are different, their potential energies at 10 m will also be different. Therefore, they do not have the same potential energy.
Kinetic Energy Comparison
- Kinetic Energy:
- Kinetic energy (KE) is given by the formula KE = 1/2 mv², where 'm' is mass and 'v' is velocity.
- As both spheres fall, they will reach different velocities by the time they are 10 m above the ground, again leading to different kinetic energies.
Conclusion
Thus, while the two spheres have the same acceleration due to gravity, their potential and kinetic energies differ due to their varying masses. Therefore, the correct answer that they have in common when they are 10 m above the ground is option 'A' - they have the same acceleration.
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An iron sphere of mass 10 kg has the same diameter as an aluminium sphere of mass 3.5 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same:a)Accelerationb)Potential energyc)Kinetic energyCorrect answer is option 'A'. Can you explain this answer?
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