Vidaara.orgClass 11 · Physics
CodeVID-P11-07-UGG-01
Universal Gravitation & g — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The SI unit of the gravitational constant $G$ is:
- A.$\text{N}\,\text{m}\,\text{kg}^{-1}$
- B.$\text{N}\,\text{m}^2\,\text{kg}^{-2}$
- C.$\text{N}\,\text{kg}^{-2}$
- D.$\text{N}\,\text{m}^{-2}$
2.
Gravitational force is:
- A.always attractive
- B.always repulsive
- C.sometimes attractive, sometimes repulsive
- D.zero between unequal masses
3.
The value of $g$ depends on:
- A.mass of the falling body
- B.shape of the falling body
- C.mass and radius of the Earth
- D.colour of the body
4.
Weight of a body at the centre of the Earth is:
- A.maximum
- B.the same as at the surface
- C.zero
- D.infinite
5.
If the radius of the Earth shrank to half with mass unchanged, $g$ would become:
- A.half
- B.double
- C.four times
- D.one-fourth
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
State Newton's law of gravitation and write its mathematical form.
7.
Why does the value of $g$ not depend on the mass of the falling body?
8.
Two masses 3 kg and 4 kg are 1 m apart. Find the force between them.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
Derive the expression for the variation of $g$ with height $h$ for $h\ll R$.
10.
At what height does $g$ reduce to 36% of its surface value? (Take $R=6400$ km.)
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Explain how the value of $g$ varies with altitude, depth and latitude. Give the relevant formulas and state where $g$ is maximum and minimum.
Answer Key
Section A — Multiple Choice Questions
- (B) $\text{N}\,\text{m}^2\,\text{kg}^{-2}$
- (A) always attractive
- (C) mass and radius of the Earth
- (C) zero
- (C) four times
Section B — Short Answer (2 marks)
- Every two point masses attract with $F=\frac{Gm_1m_2}{r^2}$, directed along the line joining them.
- Because $g=\frac{GM}{R^2}$ contains only Earth's mass and radius; the body's mass cancels from $mg=\frac{GMm}{R^2}$.
- $F=6.67\times10^{-11}\times12=8.0\times10^{-10}\ \text{N}$.
Section C — Short Answer (3 marks)
- $g_h=\frac{GM}{(R+h)^2}\approx g\left(1-\frac{2h}{R}\right)$.
- $\left(\frac{R}{R+h}\right)^2=0.36\Rightarrow\frac{R}{R+h}=0.6\Rightarrow h\approx4267\ \text{km}$.
Section D — Long Answer (5 marks)
- Altitude: $g_h=g(1-2h/R)$ (decreases up). Depth: $g_d=g(1-d/R)$ (decreases down, zero at centre). Latitude/rotation: $g_\lambda=g-R\omega^2\cos^2\lambda$; $g$ is maximum at the poles and minimum at the equator.
Generated by Vidaara.org · Assignment VID-P11-07-UGG-01 · vidaara.org