Chapter 1: Gravitation – 15 Most Important Solved Questions
Q1. State Newton’s law of universal gravitation.
Every object attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
\( F = G \frac{m_1 m_2}{r^2} \)
\( F = G \frac{m_1 m_2}{r^2} \)
Q2. Define G. State its SI unit.
G is the universal gravitational constant.
SI unit: \( \text{Nm}^2/\text{kg}^2 \), Value: \( 6.674 \times 10^{-11} \ \text{Nm}^2/\text{kg}^2 \)
SI unit: \( \text{Nm}^2/\text{kg}^2 \), Value: \( 6.674 \times 10^{-11} \ \text{Nm}^2/\text{kg}^2 \)
Q3. What if distance is doubled?
\( F' = \frac{F}{4} \) — force becomes one-fourth.
Q4. Value and unit of g on Earth?
\( g = 9.8 \ \text{m/s}^2 \)
Q5. Relation between g and G?
\( g = \frac{G M}{R^2} \)
Q6. How g changes with height?
g decreases with increase in height.
Q7. Derive gravity formula.
\( F = G \frac{M m}{R^2} \), so \( g = \frac{G M}{R^2} \)
Q8. Drop from 20 m: Time?
\( h = 20, u = 0, g = 10 \) → \( t = \sqrt{\frac{2h}{g}} = \sqrt{4} = 2 \ \text{s} \)
Q9. Mass vs Weight?
Mass: constant (kg); Weight: \( W = mg \), varies with gravity.
Q10. Free fall? Acceleration?
Motion under gravity only. Acceleration = \( g = 9.8 \ \text{m/s}^2 \)
Q11. Derive \( v = u + gt \)
From motion equation: \( v = u + at \), here \( a = g \)
Q12. Why g varies across planets?
\( g = \frac{G M}{R^2} \) — M, R differ for each planet.
Q13. Force between two 1 kg masses 1 m apart?
\( F = G \frac{1 \cdot 1}{1^2} = 6.674 \times 10^{-11} \ \text{N} \)
Q14. Weight of 2 kg on Moon (g = 1.63)?
\( W = mg = 2 \cdot 1.63 = 3.26 \ \text{N} \)
Q15. Why weight is zero in space?
\( W = mg \), and in space \( g \approx 0 \), so \( W = 0 \)