Science and Technology I · Textbook solutions

Gravitation

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 15 questions

Exercise

15 q
  1. Ex Q1
    Study the entries in the following table and rewrite them putting the connected items in a single row.
    IIIIII
    Massm/s²Zero at the centre
    WeightkgMeasure of inertia
    Acceleration due to gravityNm²/kg²Same in the entire universe
    Gravitational constantNDepends on height
  2. Answer the following questions.
    Ex Q2(a)
    What is the difference between mass and weight of an object. Will the mass and weight of an object on the earth be same as their values on Mars? Why?
  3. Ex Q2(b)
    What are (i) free fall, (ii) acceleration due to gravity (iii) escape velocity (iv) centripetal force ?
  4. Ex Q2(c)
    Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
  5. Ex Q2(d)
    A stone thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is same as the time taken to come down.
  6. Ex Q2(e)
    If the value of g suddenly becomes twice its value, it will become two times more difficult to pull a heavy object along the floor. Why?
  7. Ex Q3
    Explain why the value of g is zero at the centre of the earth.
  8. Ex Q4
    Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be 8 T\sqrt{8}\,T.
  9. Solve the following examples.
    Ex Q5(a)
    An object takes 5 s to reach the ground from a height of 5 m on a planet. What is the value of g on the planet?
  10. Ex Q5(b)
    The radius of planet A is half the radius of planet B. If the mass of A is MAM_A, what must be the mass of B so that the value of g on B is half that of its value on A?
  11. Ex Q5(c)
    The mass and weight of an object on earth are 5 kg and 49 N respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is 1/6th of that on the earth.
  12. Ex Q5(d)
    An object thrown vertically upwards reaches a height of 500 m. What was its initial velocity? How long will the object take to come back to the earth? Assume g=10 m/s2g = 10\ \text{m/s}^2.
  13. Ex Q5(e)
    A ball falls off a table and reaches the ground in 1 s. Assuming g=10 m/s2g = 10\ \text{m/s}^2, calculate its speed on reaching the ground and the height of the table.
  14. Ex Q5(f)
    The masses of the earth and moon are 6×10246 \times 10^{24} kg and 7.4×10227.4 \times 10^{22} kg, respectively. The distance between them is 3.84×1053.84 \times 10^{5} km. Calculate the gravitational force of attraction between the two? Use G=6.7×10−11 N m2 kg−2G = 6.7 \times 10^{-11}\ \text{N m}^2\,\text{kg}^{-2}.
  15. Ex Q5(g)
    The mass of the earth is 6×10246 \times 10^{24} kg. The distance between the earth and the Sun is 1.5×10111.5 \times 10^{11} m. If the gravitational force between the two is 3.5×10223.5 \times 10^{22} N, what is the mass of the Sun? Use G=6.7×10−11 N m2 kg−2G = 6.7 \times 10^{-11}\ \text{N m}^2\,\text{kg}^{-2}.