Acceleration due to Gravity and Its Variation - UNSOLVED PRACTICE SET

Q7. Derive the expression for acceleration due to gravity on the surface of the Earth in terms of G, M, and R.

Q8. Explain why the value of g is less at the equator than at the poles. Consider both the shape of the Earth and its rotation.

Q9. Calculate the value of g at a height of 320 km above Earth's surface. (R = 6400 km, g = 9.8 m/s²)

Q10. In your school, a student claims that a weighing machine would show the same reading at the top of Qutub Minar (73 m high) and at ground level. Is this correct? Calculate the percentage difference in weight.

Q11. Derive the expression for g at depth d below Earth's surface, assuming uniform density.here...

Q12. Why does a body weigh slightly less on a mountain top than at sea level? Does its mass also change?

Q13. Discuss the variation of acceleration due to gravity with:

(i) Altitude above Earth's surface (derive for h << R and for any height)

(ii) Depth below Earth's surface

(iii) Latitude due to Earth's rotation

(iv) Shape of the Earth

Draw graphs showing g vs h and g vs d. Explain why g is minimum at the equator and maximum at the poles.

Q14. A body weighs 98 N on the surface of the Earth.

(a) Calculate its mass.

(b) Calculate its weight at a height equal to half the Earth's radius.

(c) Calculate its weight at a depth equal to one-fourth the Earth's radius.

(d) Calculate its weight at the equator, considering Earth's rotation. (ω = 7.27 × 10⁻⁵ rad/s)

(e) At what height above the equator would the body weigh the same as at the pole?

Q15. Analyse the following statement: "If Earth stopped rotating, the value of g would be the same everywhere on the surface." Is this true? Discuss the factors that would still cause variation in g even without rotation.

Q16. A pendulum clock accurate at sea level is taken to:

(a) A hill station at 2000 m above sea level. Does it gain or lose time? Calculate the time lost/gained in one day.

(b) A mine 1000 m deep. Does it gain or lose time? Calculate the time lost/gained in one day.

(c) The equator from the pole. Does it gain or lose time?

(d) Explain why a pendulum clock cannot be used to measure time accurately at different locations without adjustment.

Q17. The radius of Earth is 6400 km and g at the surface is 9.8 m/s².

(a) Calculate g at a height of 640 km above the surface.

(b) Calculate g at a depth of 1600 km below the surface.

(c) At what height above the surface is g equal to 4.9 m/s²?

(d) At what depth below the surface is g equal to 4.9 m/s²?

(e) Compare your answers for (c) and (d) and explain why they are different.

Q18. In a school project, students want to measure g at different locations in Delhi.

(a) Design an experiment using a simple pendulum to measure g.

(b) If the pendulum length is 1 m and it completes 50 oscillations in 100.5 seconds at one location, calculate g at that location.

(c) At another location, the same pendulum completes 50 oscillations in 100.2 seconds. Calculate the difference in g.

(d) What factors could cause this small difference within the same city?

(e) How would you improve the accuracy of this measurement?