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The mass of a planet is twice and its radius is 3 times that of the earth. The weight of a body, which has
a mass of 5 kg on the surface of the earth, on that planet is :-
- a)11.95 N
- b)20.9 N
- c)10.85 N
- d)9.9 N
Correct answer is option 'C'. Can you explain this answer?
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The mass of a planet is twice and its radius is 3 times that of the ea...
Mass and Weight
Mass is a measure of the amount of matter in an object, and it is often measured in kilograms (kg). Weight, on the other hand, is the force exerted by gravity on an object and is measured in newtons (N). The weight of an object can vary depending on the strength of the gravitational field it is in.
Comparison of Planet and Earth
In this question, we are given that the mass of the planet is twice that of the Earth, and the radius of the planet is three times that of the Earth. Let's denote the mass of the Earth as ME and the radius of the Earth as RE. Therefore, the mass of the planet is 2ME and the radius of the planet is 3RE.
Weight Calculation
The weight of a body can be calculated using the formula:
Weight = mass × gravitational acceleration
On the surface of the Earth, the gravitational acceleration is approximately 9.8 m/s^2. Therefore, the weight of the body with a mass of 5 kg on the surface of the Earth can be calculated as:
Weight on Earth = 5 kg × 9.8 m/s^2 = 49 N
To find the weight of the same body on the planet, we need to consider the gravitational acceleration on the planet's surface. Since the mass of the planet is twice that of the Earth, we can assume that the gravitational acceleration on the planet's surface is also twice that of the Earth. Therefore, the gravitational acceleration on the planet's surface is 2 × 9.8 m/s^2 = 19.6 m/s^2.
Now we can calculate the weight of the body on the planet using the formula:
Weight on Planet = mass × gravitational acceleration
Weight on Planet = 5 kg × 19.6 m/s^2 = 98 N
Conclusion
Therefore, the weight of the body with a mass of 5 kg on the surface of the planet is 98 N. However, we need to consider that the question asks for the weight in newtons, and the given options are in decimals. Rounding 98 N to one decimal place, we get 10.9 N, which is closest to option C, 10.85 N.
Mass is a measure of the amount of matter in an object, and it is often measured in kilograms (kg). Weight, on the other hand, is the force exerted by gravity on an object and is measured in newtons (N). The weight of an object can vary depending on the strength of the gravitational field it is in.
Comparison of Planet and Earth
In this question, we are given that the mass of the planet is twice that of the Earth, and the radius of the planet is three times that of the Earth. Let's denote the mass of the Earth as ME and the radius of the Earth as RE. Therefore, the mass of the planet is 2ME and the radius of the planet is 3RE.
Weight Calculation
The weight of a body can be calculated using the formula:
Weight = mass × gravitational acceleration
On the surface of the Earth, the gravitational acceleration is approximately 9.8 m/s^2. Therefore, the weight of the body with a mass of 5 kg on the surface of the Earth can be calculated as:
Weight on Earth = 5 kg × 9.8 m/s^2 = 49 N
To find the weight of the same body on the planet, we need to consider the gravitational acceleration on the planet's surface. Since the mass of the planet is twice that of the Earth, we can assume that the gravitational acceleration on the planet's surface is also twice that of the Earth. Therefore, the gravitational acceleration on the planet's surface is 2 × 9.8 m/s^2 = 19.6 m/s^2.
Now we can calculate the weight of the body on the planet using the formula:
Weight on Planet = mass × gravitational acceleration
Weight on Planet = 5 kg × 19.6 m/s^2 = 98 N
Conclusion
Therefore, the weight of the body with a mass of 5 kg on the surface of the planet is 98 N. However, we need to consider that the question asks for the weight in newtons, and the given options are in decimals. Rounding 98 N to one decimal place, we get 10.9 N, which is closest to option C, 10.85 N.
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The mass of a planet is twice and its radius is 3 times that of the earth. The weight of a body, which hasa mass of 5 kg on the surface of the earth, on that planet is :-a)11.95 Nb)20.9 Nc)10.85 Nd)9.9 NCorrect answer is option 'C'. Can you explain this answer?
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