NEET Gravitation — Set 20

Question 1

Two masses $ 10 \, \text{kg} $ and $ 20 \, \text{kg} $ are $ 20 \, \text{m} $ apart. What is the gravitational potential at a point $ 9 \, \text{m} $ from the $ 10 \, \text{kg} $ mass? ($ G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 $)

Accepted Answer

Distance to $ 20 \, \text{kg} $: $ 20 - 9 = 11 \, \text{m} $. $ U = -\frac{G m_1}{r_1} - \frac{G m_2}{r_2} $. $ U = -6.67 \times 10^{-11} \left(\frac{10}{9} + \frac{20}{11}\right) $. $ U = -6.67 \times 10^{-11} (1.111 + 1.818) \approx -1.95 \times 10^{-10} \, \text{J/kg} $.

Question 2

A projectile is launched from Earth with a speed of $ 15 \, \text{km/s} $. What is its speed at infinity? (Escape speed = $ 11.2 \, \text{km/s} $)

Accepted Answer

Total energy: $ E = \frac{1}{2} m v_i^2 - \frac{G M_E m}{R_E} $. At infinity: $ E = \frac{1}{2} m v_f^2 $, $ v_e = \sqrt{\frac{2 G M_E}{R_E}} $. $ \frac{1}{2} v_i^2 - \frac{1}{2} v_e^2 = \frac{1}{2} v_f^2 $. $ v_f^2 = (15)^2 - (11.2)^2 = 225 - 125.44 = 99.56 $. $ v_f = \sqrt{99.56} \approx 10 \, \text{km/s} $.

Question 3

Which of the following statements is incorrect about gravitational force?

Accepted Answer

Gravitational force is always attractive (option 2 is correct), follows the inverse-square law (option 3 is correct), and acts between all masses (option 4 is correct). Option 1 is incorrect as it can be zero inside a shell.

NEET Physics: Gravitation — Practice Set 20

Q1. Two masses \( 10 \, \text{kg} \) and \( 20 \, \text{kg} \) are \( 20 \, \text{m} \) apart. What is the gravitational potential at a point \( 9 \, \text{m} \) from the \( 10 \, \text{kg} \) mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q2. A projectile is launched from Earth with a speed of \( 15 \, \text{km/s} \). What is its speed at infinity? (Escape speed = \( 11.2 \, \text{km/s} \))

Q3. Which of the following statements is incorrect about gravitational force?

Q4. What is the key assumption about Earth’s density in calculating \( g \) below its surface?

Q5. At what height above Earth’s surface is \( g \) reduced to \( 8.82 \, \text{m/s}^2 \)? (\( g_0 = 9.8 \, \text{m/s}^2, R_E = 6.4 \times 10^6 \, \text{m} \))

Q6. Two identical masses of \( 5 \, \text{kg} \) each are placed at the vertices A and B of an equilateral triangle ABC with side length \( 2 \, \text{m} \). What is the gravitational force on a \( 10 \, \text{kg} \) mass at vertex C? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q7. Four equal masses of \( 3 \, \text{kg} \) are at the vertices of a square with side \( 2 \, \text{m} \). What is the net force on one mass? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q8. How much energy is required to move a \( 500 \, \text{kg} \) satellite from \( 5 R_E \) to \( 10 R_E \) from Earth’s center? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q9. A \( 1100 \, \text{kg} \) satellite orbits Earth at \( 18 R_E \) from the center. What is its total energy? (\( M_E = 6 \times 10^{24} \, \text{kg}, R_E = 6.4 \times 10^6 \, \text{m}, G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

Q10. What is the gravitational force on a \( 10 \, \text{kg} \) mass \( 8 \, \text{m} \) from the center of a spherical shell of mass \( 450 \, \text{kg} \) and radius \( 6 \, \text{m} \)? (\( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))