If a body of mass ‘m’ is taken to a height ‘h’ from the surface of earth, the work done will be:

The correct answer is mgh.

Key Points

• The work done to take a body of mass ‘m’ to a height ‘h’ is equal to the change in gravitational potential energy, which is calculated as W = mgh.
• Gravitational potential energy depends on the mass of the body (m), acceleration due to gravity (g), and the height (h) from the reference point.
• This formula assumes that the gravitational force is constant, which is a valid approximation near the Earth's surface.
• The correct option, mgh, signifies the direct proportionality of work done to mass and height when moving a body against gravity.
• This concept is widely used in physics to calculate energy transformations in systems involving gravitational forces.

Additional Information

• Gravitational Potential Energy:
  • It is the energy possessed by an object due to its position relative to Earth or another gravitational source.
  • Formula: U = mgh, where ‘U’ is potential energy, ‘m’ is mass, ‘g’ is acceleration due to gravity, and ‘h’ is height.
• Work Done Against Gravity:
  • Work is defined as the energy required to move a body against a force—in this case, gravitational force.
  • The work done is calculated using W = Force × Distance, which simplifies to W = mgh for gravitational systems.
• Acceleration Due to Gravity (g):
  • The value of ‘g’ near Earth's surface is approximately 9.8 m/s².
  • It influences the weight of objects and the work required to move them vertically.
• Conservation of Energy:
  • When a body is lifted, its mechanical energy is conserved, transitioning from kinetic energy to potential energy.
  • Gravitational potential energy plays a key role in systems like pendulums and roller coasters.