NEET Gravitation — Set 25

Question 1

A body weighs $ 294 \, \text{N} $ on Earth’s surface. What is its weight at a height $ h = 3 R_E/4 $? ($ g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} $)

Accepted Answer

$ g(h) = \frac{g}{(1 + h/R_E)^2} $. $ h = 3 R_E/4 $, $ 1 + h/R_E = 1 + 3/4 = 7/4 $. $ g(h) = \frac{9.8}{(7/4)^2} = 9.8 \times \frac{16}{49} = 3.2 \, \text{m/s}^2 $. Mass: $ m = 294/9.8 = 30 \, \text{kg} $. Weight: $ W = 30 \times 3.2 = 96 \, \text{N} $.

Question 2

Which of the following statements is incorrect about escape speed?

Accepted Answer

Escape speed depends on planet parameters (option 1 correct), is independent of direction (option 3 correct), and mass (option 4 correct). Option 2 is incorrect as it decreases with altitude.

Question 3

A body weighs $ 147 \, \text{N} $ on Earth’s surface. What is its weight at a height $ h = R_E/3 $? ($ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

$ g(h) = \frac{g}{(1 + h/R_E)^2} $. $ h = R_E/3 $, $ 1 + h/R_E = 4/3 $. $ g(h) = \frac{9.8}{(4/3)^2} = 9.8 \times \frac{9}{16} = 5.51 \, \text{m/s}^2 $. Mass: $ m = 147/9.8 = 15 \, \text{kg} $. Weight: $ W = 15 \times 5.51 \approx 82.7 \, \text{N} $.

NEET Physics: Gravitation — Practice Set 25

Q1. A body weighs \( 294 \, \text{N} \) on Earth’s surface. What is its weight at a height \( h = 3 R_E/4 \)? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q2. Which of the following statements is incorrect about escape speed?

Q3. A body weighs \( 147 \, \text{N} \) on Earth’s surface. What is its weight at a height \( h = R_E/3 \)? (\( g = 9.8 \, \text{m/s}^2 \))

Q4. What ensures that a planet moves faster at perihelion than at aphelion?

Q5. At what height above Earth’s surface is \( g \) reduced to \( 5.88 \, \text{m/s}^2 \)? (\( g_0 = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q6. A planet orbits the Sun with a period of 5 years. If Earth’s orbital radius is \( 1.5 \times 10^{11} \, \text{m} \), what is its semi-major axis?

Q7. A satellite orbits a planet at \( 8 \times 10^7 \, \text{m} \) from its center with a period of 20 hours. What is the planet’s mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q8. A satellite orbits Earth at \( 2.5 R_E \) from the center. What is its orbital speed? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q9. What is the minimum speed to escape from \( 5 R_E \) from Earth’s center? (\( g = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q10. What is the physical significance of the gravitational constant \( G \) in Newton’s law?