PHYSICS

A STONE OF MASS 1KG IS DROPPED FROM A HEIGHT OF 10M ABOVE THE GROUND AND FALLS FREELY UNDER GRAVITY. ITS KINETIC ENERGY 5M ABOVE THE GROUND IS THEN EQUAL TO

  • A. its kinetic energy on the ground
  • B. twice its initial potential energy
  • C. its initial potential energy
  • D. half its initial potential energy ✓

 

When the stone is dropped from a height of 10m above the ground, it possesses gravitational potential energy due to its position above the ground. As it falls freely under gravity, this potential energy is converted into kinetic energy.

The potential energy of an object at a height h above the ground can be calculated using the formula:

PE = mgℎ

Where:

  • PE is the potential energy,
  • m is the mass of the object (1kg in this case),
  • g is the acceleration due to gravity (approximately 9.81 m/s² on Earth),
  • h is the height above the ground (initially 10m).

Given that the stone is dropped from rest, its initial kinetic energy is zero. As it falls, its potential energy decreases while its kinetic energy increases. At any point during the fall, the total mechanical energy (sum of kinetic and potential energies) remains constant in the absence of non-conservative forces like air resistance.

When the stone is 5m above the ground, half of its initial potential energy has been converted into kinetic energy. This can be understood by considering that at half the initial height, half of the potential energy has been used up and converted into kinetic energy.

Therefore, at 5m above the ground, the stone’s kinetic energy is equal to half of its initial potential energy.

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