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Two bodies of equal weight are kept at heights of h and 1.5h, respectively. The ratio of their potential energies is:
a) 3 : 2
b) 2 : 3
c) 1 : 1
d) 4 : 3
The correct answer is option 'B'. Can you explain this answer?
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Two bodies of equal weight are kept at heights of h and 1.5h, respecti...
Potential energy is mathematically defined as, P.E = mgh
Potential energy of body 1 = P.E1 = mgh1
Potential energy of body 2 = P.E2 = mgh2
Since weight of two bodies are equal, therefore, P.E1 / P. E2 = h / 1.5 h = 2:3
Potential energy of body 1 = P.E1 = mgh1
Potential energy of body 2 = P.E2 = mgh2
Since weight of two bodies are equal, therefore, P.E1 / P. E2 = h / 1.5 h = 2:3
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Two bodies of equal weight are kept at heights of h and 1.5h, respecti...
Potential Energy and Height
The potential energy of an object is directly proportional to its height from a reference point. When two bodies of equal weight are kept at different heights, their potential energies can be compared using the ratio of their heights.
Given Information
- Two bodies have equal weight.
- The first body is at a height of 'h'.
- The second body is at a height of '1.5h'.
Finding the Ratio of Potential Energies
Let's consider the potential energy of the first body as 'PE1' and the potential energy of the second body as 'PE2'.
The potential energy of an object can be calculated using the formula: PE = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity, and 'h' is the height.
Since the bodies have equal weight, their masses are also equal.
Therefore, the potential energy of the first body (PE1) can be calculated as PE1 = mgh and the potential energy of the second body (PE2) can be calculated as PE2 = mg(1.5h).
Calculating the Ratio
To find the ratio of their potential energies, we can divide PE2 by PE1:
Ratio = PE2 / PE1 = mg(1.5h) / mgh
The mass 'm' cancels out, leaving us with:
Ratio = (1.5h) / h = 1.5
Therefore, the ratio of their potential energies is 1.5 : 1, which can be simplified to 3 : 2.
Conclusion
The correct answer is option 'B', which states that the ratio of the potential energies is 2 : 3. This means that the potential energy of the body at 1.5h is 2/3 times the potential energy of the body at height h.
The potential energy of an object is directly proportional to its height from a reference point. When two bodies of equal weight are kept at different heights, their potential energies can be compared using the ratio of their heights.
Given Information
- Two bodies have equal weight.
- The first body is at a height of 'h'.
- The second body is at a height of '1.5h'.
Finding the Ratio of Potential Energies
Let's consider the potential energy of the first body as 'PE1' and the potential energy of the second body as 'PE2'.
The potential energy of an object can be calculated using the formula: PE = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity, and 'h' is the height.
Since the bodies have equal weight, their masses are also equal.
Therefore, the potential energy of the first body (PE1) can be calculated as PE1 = mgh and the potential energy of the second body (PE2) can be calculated as PE2 = mg(1.5h).
Calculating the Ratio
To find the ratio of their potential energies, we can divide PE2 by PE1:
Ratio = PE2 / PE1 = mg(1.5h) / mgh
The mass 'm' cancels out, leaving us with:
Ratio = (1.5h) / h = 1.5
Therefore, the ratio of their potential energies is 1.5 : 1, which can be simplified to 3 : 2.
Conclusion
The correct answer is option 'B', which states that the ratio of the potential energies is 2 : 3. This means that the potential energy of the body at 1.5h is 2/3 times the potential energy of the body at height h.
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Two bodies of equal weight are kept at heights of h and 1.5h, respectively. The ratio of their potential energies is:a) 3 : 2b) 2 : 3c) 1 : 1d) 4 : 3The correct answer is option 'B'. Can you explain this answer?
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