Correct Answer - Option 2 : Person moving on hill
CONCEPT:
Kinetic Energy
- The energy possessed by a particle by the virtue of its motion is called kinetic energy. It is given by,
\(⇒ KE=\frac{1}{2}m× v^{2}\)
Gravitational Potential Energy
- The energy possessed by a body by virtue of its position is known as gravitational potential energy.
- When the object reaches to height h from the surface of the earth, its gravitational potential energy will be increased by,
\(\Rightarrow PE=mgh\)
Where KE = kinetic energy, PE = change in potential energy, m = mass and v = velocity
Mechanical energy
- The energy possessed by a body due to its state of rest or state of motion.
\(\Rightarrow Total\,ME=KE+PE\)
Where ME = mechanical energy
EXPLANATION:
- Since the mass and the velocity of both the person are equal so the kinetic energy of both the person is also equal.
- The person who is moving on a hill is at more height compared to the person at sea level, so the person at the hill will have more potential energy.
\(\Rightarrow KE_{S}=KE_{H}=KE\)
\(\Rightarrow PE_{S}<PE_{H}\) -----(1)
- For the person at sea level,
\(\Rightarrow Total\,ME_{S}=KE_{S}+PE_{S}\)
\(\Rightarrow Total\,ME_{S}=KE+PE_{S}\) -----(2)
For the person at the hill,
\(\Rightarrow Total\,ME_{H}=KE+PE_{H}\) -----(3)
By equation 1, equation 2, and equation 3,
\(\Rightarrow Total\,ME_{S}<Total\,ME_{H}\)
- So the person moving on a hill will have more mechanical energy.
- Hence, option 2 is correct.
