NEET Gravitation — Set 6

Question 1

Two masses $ 2 \, \text{kg} $ and $ 8 \, \text{kg} $ are separated by $ 4 \, \text{m} $. What is the gravitational potential at the midpoint? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

Distance to midpoint: $ r = 2 \, \text{m} $. $ U = -\frac{G m_1}{r} - \frac{G m_2}{r} $. $ U = -6.67 \times 10^{-11} \left(\frac{2}{2} + \frac{8}{2}\right) $. $ U = -6.67 \times 10^{-11} \times (1 + 4) = -3.335 \times 10^{-10} \, \text{J/kg} $.

Question 2

Which of the following statements is correct about gravitational potential energy?

Accepted Answer

$ V = -\frac{G M m}{r} $, which is negative for bound systems and decreases (becomes more negative) as $ r $ decreases, making option 3 correct.

Question 3

Why does the Moon’s orbital period relate to Earth’s mass?

Accepted Answer

Kepler’s third law ($ T^2 = \frac{4\pi^2}{G M_E} r^3 $) to satellites like the Moon, where the period $ T $ depends on Earth’s mass $ M_E $, the central body, determining the gravitational force strength.

NEET Physics: Gravitation — Practice Set 6

Q1. Two masses \( 2 \, \text{kg} \) and \( 8 \, \text{kg} \) are separated by \( 4 \, \text{m} \). What is the gravitational potential at the midpoint? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q2. Which of the following statements is correct about gravitational potential energy?

Q3. Why does the Moon’s orbital period relate to Earth’s mass?

Q4. What determines whether an object can escape Earth’s gravitational influence?

Q5. A projectile is launched at \( 3 \, \text{km/s} \) from Earth’s surface. What is its maximum distance from the center? (Escape speed = \( 11.2 \, \text{km/s}, R_E = 6.4 \times 10^6 \, \text{m} \))

Q6. A body weighs \( 343 \, \text{N} \) on Earth’s surface. What is its weight at a height \( h = R_E/5 \)? (\( g = 9.8 \, \text{m/s}^2 \))

Q7. Which of the following statements is incorrect about gravitational potential energy?

Q8. Three \( 6 \, \text{kg} \) masses form an equilateral triangle of side \( 8 \, \text{m} \). What is the potential energy of the system? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

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

Q10. Three masses of \( 10 \, \text{kg} \) each form an equilateral triangle with side \( 7 \, \text{m} \). What is the net force on one mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))