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| Acceleration due to Gravity on Moon |
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| The expression for acceleration due to gravity is |
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| Where G is the universal gravitational constant, M is the mass of the celestial body which produces acceleration in a body and R is the radius of the celestial body. |
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| The equation for g shows that the value of acceleration due to gravity depends on the mass and radius of the celestial body and hence will be different for different celestial bodies. |
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| Let us now derive a relation between the acceleration due to gravity on moon (gm) and acceleration due to gravity on Earth (ge). |
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| Where Me and Re are the mass and radius of the Earth respectively. |
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| Where Mm and Rm are the mass and radius of the moon respectively. |
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| Divide equation (1) by equation (2) |
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| We know that mass of the Earth is 100 times that of the moon and its radius is four times that of the moon. |
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| i.e., |
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| Me = 100 Mm |
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| Re = 4 Rm |
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| Which means that acceleration due to gravity on moon is 1/6th that on the Earth. |
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| 01. The Earth's gravitational force causes an acceleration of 5 m/s2 in a 1 kg mass somewhere in space. How much will the acceleration of a 3 kg mass be at the same place? |
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| Solution: |
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| The acceleration produced in any body due to the gravitational pull of the Earth does not depend on the mass of the body. So the acceleration produced in the |
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| 3 kg mass will also be 5 m/s2. |
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| 02. Calculate the height of a bridge if a stone dropped from it takes six seconds to touch the surface of water. |
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| Solution: |
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| Initial velocity (u) = 0 |
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| Time taken (t) = 6 seconds |
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| Acceleration due to gravity (g) = 9.8 m/s2 |
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| We make use of second equation of motion |
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| h = 0 + 4.9 x 36 |
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| h = 176.4 m |
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| 03. A stone projected vertically upward, takes 5 seconds to reach the highest point. What is the initial velocity of the stone? |
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| Solution: |
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| Time taken = 5 seconds |
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| Final velocity (v) = 0 (at maximum height velocity will be equal to zero) |
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| v = u + gt |
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| 0 = u - 9.8 x 5 |
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| 0 = u - 49.0 |
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| u = 49 m/s |
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| Initial velocity = 49 m/s. |
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