NEET Gravitation — Set 18

Question 1

A moon orbits a planet with a period of 6 days and radius $ 4 \times 10^8 \, \text{m} $. What is the planet’s mass? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s} $)

Accepted Answer

$ M = \frac{4\pi^2 r^3}{G T^2} $. $ T = 6 \times 86400 = 5.184 \times 10^5 \, \text{s} $. $ T^2 = 2.689 \times 10^{11} \, \text{s}^2 $. $ r^3 = (4 \times 10^8)^3 = 6.4 \times 10^{25} \, \text{m}^3 $. $ M = \frac{4 \times (3.14)^2 \times 6.4 \times 10^{25}}{6.67 \times 10^{-11} \times 2.689 \times 10^{11}} $. $ M = \frac{2.523 \times 10^{26}}{1.794 \times 10^1} \approx 1.41 \times 10^{25} \, \text{kg} $.

Question 2

What is the significance of the Cavendish experiment in understanding gravity?

Accepted Answer

Correct option: B

Question 3

Why does a satellite in a higher orbit have a longer orbital period?

Accepted Answer

$ T^2 \propto r^3 $ for satellites. A higher orbit (larger $ r $) increases $ T^2 $ by $ r^3 $, so the period $ T $ increases as the radius grows, reflecting weaker gravitational pull at greater distances.

NEET Physics: Gravitation — Practice Set 18

Q1. A moon orbits a planet with a period of 6 days and radius \( 4 \times 10^8 \, \text{m} \). What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s} \))

Q2. What is the significance of the Cavendish experiment in understanding gravity?

Q3. Why does a satellite in a higher orbit have a longer orbital period?

Q4. A moon orbits a planet with a period of 12 days and radius \( 9 \times 10^8 \, \text{m} \). What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s} \))

Q5. What is the total energy of a \( 100 \, \text{kg} \) satellite orbiting Earth at \( 3 R_E \) from the center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q6. Why does the gravitational potential decrease (become less negative) as altitude increases?

Q7. Why does the gravitational potential energy depend on the inverse of distance?

Q8. What is the gravitational potential at a point \( 9.6 \times 10^6 \, \text{m} \) from Earth’s center due to Earth? (\( M_E = 6 \times 10^{24} \, \text{kg}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q9. A moon orbits a planet with a period of 11 days and radius \( 8 \times 10^8 \, \text{m} \). What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2, 1 \, \text{day} = 86400 \, \text{s} \))

Q10. What does the variation of \( g \) with altitude indicate about gravitational force?