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2 years ago

How high above the ground would a 10 kg object needs to be to have the same GPE as the 30 kg object in the example

Physics

1 answer:

Black_prince [1.1K]2 years ago

4 0

Answer:

The 10 kg mass would have to be at a height 3 times that of the 30 kg mass to have the same gravitational potential energy as the 30 kg mass.

Explanation:

Gravitational potential energy, U = mgh where m = mass of object, g = acceleration due to gravity = 9.8 m/s² and h = height of object above the ground.

Now, let U' = gravitational potential energy of 10 kg mass = m'gh' where m' = 10 kg and h' = height of 10 kg mass above the ground.

So, U' = 10gh'

Also, let U" = gravitational potential energy of 30 kg mass = m"gh" where m" = 30 kg and h" = height of 30 kg mass above the ground.

So, U" = 30gh"

Since both object are supposed to have the same potential energy at a given height of the 10 kg mass,

U' = U"

10gh' = 30gh"

h' = 30gh"/10g

h' = 3h"

<u>So, the 10 kg mass would have to be at a height 3 times that of the 30 kg mass to have the same gravitational potential energy as the 30 kg mass.</u>

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Answer:

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Mathematically it can be written as $T^{2} \alpha R^{3}$

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Here K is the proportionality constant.

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$\frac{T_{1} ^{2} }{T_{2} ^{2} } =\frac{R_{1} ^{3} }{R_{2} ^{2} }$

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Here we are asked to calculate the the distance of Saturn from sun.It can solved by comparing it with earth.

Let the distance from sun and orbital period of Saturn is denoted as $R_{1}$ and $T_{1}$ respectively.

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Hence distance of Saturn from sun is calculated as -

From Kepler's law as mentioned above-

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= $[1 ]^{3} *\frac{[29.46]^{2} }{[1]^{2} } AU$

$=867.8916 AU^{3}$

⇒ $R_{1} =\sqrt[3]{867.8916}$

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