When a body is dropped from the same height on surface of moon and the earth, the ratio of time to reach the ground will be.
pls explain this q
the ans is showing root 6: 1.
Answers
Answer: Any object that is only acted on by the force of gravity is said to be in a free fall state. Air resistance is not experienced by free-falling objects. The time taken by the same body released from the same height to reach the moon's surface is √6t.
The ratio of time taken by a body to reach the ground when dropped from the same height on the surface of the moon and the earth = 6 : 1.
→ Basic concept used:
Gravitational force between = Gravitational * Product of
two masses constant masses
Square of Distance between them
Let G be the gravitational constant.
Let m₁ be the mass of first object.
Let m₂ be the mass of second object.
Let d be the distance between the objects.
⇒ Gravitational force between objects = G * m₁ * m₂
d²
- Here, the same object/body is dropped. Therefore, mass of the body dropped remains same.
- Given that the body is dropped from the same height hence the distance is also the same.
- So, from the above formula we see that the gravitational force between the objects in this case is majorly determined by the mass of the moon and the earth.
- Gravitational force between objects ∝ Mass of earth and moon.
→ Mass of the earth is 6 times as that of the moon and hence the gravitational force of the earth will be 6 times than that of moon and hence the acceleration of the object on earth is 6 times more than that on the moon i.e., speed of the object falling on the earth will be 6 times faster as that on moon.
⇒ Time taken by the object to reach moon will be 6 times more as compared to earth.
⇒ The ratio of time taken by the object to reach the ground when dropped from the same height on the moon and earth = 6 : 1.
#SPJ2