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What is the weight of a 700 g of body on a planet whose is 1/7 th of that of earth and radius is 1/2 times of earth ?
- a)400 gf
- b)300 gf
- c)700 gf
- d)500 gf
Correct answer is option 'A'. Can you explain this answer?
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What is the weight of a 700 g of body on a planet whose is 1/7 th of t...
**Given data:**
Mass of the body = 700 g
Acceleration due to gravity on the planet = 1/7 times that of Earth
Radius of the planet = 1/2 times that of Earth
**Step 1: Calculate the weight of the body on Earth**
Weight = mass x acceleration due to gravity on Earth
Weight on Earth = 700 g x 9.8 m/s^2 (acceleration due to gravity on Earth)
Weight on Earth = 700 x 9.8/1000 ≈ 6.86 N
**Step 2: Calculate the acceleration due to gravity on the planet**
Acceleration due to gravity on the planet = 1/7 x 9.8 ≈ 1.4 m/s^2
**Step 3: Calculate the weight of the body on the planet**
Weight on the planet = mass x acceleration due to gravity on the planet
Weight on the planet = 700 g x 1.4 m/s^2
Weight on the planet = 700 x 1.4/1000 ≈ 0.98 N
**Step 4: Convert the weight on the planet to grams**
Weight on the planet = 0.98 N x 1000/9.8 ≈ 100 gf
Therefore, the weight of the 700 g body on a planet with 1/7th the gravity and 1/2 the radius of Earth is approximately 100 gf, which is closest to option A (400 gf).
Mass of the body = 700 g
Acceleration due to gravity on the planet = 1/7 times that of Earth
Radius of the planet = 1/2 times that of Earth
**Step 1: Calculate the weight of the body on Earth**
Weight = mass x acceleration due to gravity on Earth
Weight on Earth = 700 g x 9.8 m/s^2 (acceleration due to gravity on Earth)
Weight on Earth = 700 x 9.8/1000 ≈ 6.86 N
**Step 2: Calculate the acceleration due to gravity on the planet**
Acceleration due to gravity on the planet = 1/7 x 9.8 ≈ 1.4 m/s^2
**Step 3: Calculate the weight of the body on the planet**
Weight on the planet = mass x acceleration due to gravity on the planet
Weight on the planet = 700 g x 1.4 m/s^2
Weight on the planet = 700 x 1.4/1000 ≈ 0.98 N
**Step 4: Convert the weight on the planet to grams**
Weight on the planet = 0.98 N x 1000/9.8 ≈ 100 gf
Therefore, the weight of the 700 g body on a planet with 1/7th the gravity and 1/2 the radius of Earth is approximately 100 gf, which is closest to option A (400 gf).
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