Vidaara.orgClass 9 · Physics
CodeVID-P9-03-CT
Gravitation — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Take $G = 6.67 \times 10^{-11}\ \text{N m}^2/\text{kg}^2$, $g = 10\ \text{m/s}^2$ and density of water $= 1000\ \text{kg/m}^3$ unless stated. Show all working for Sections B, C and D.
Section A — Multiple Choice Questions
6 × 1 = 6 marks
1.
Gravitational force varies with distance as:
- A.$r$
- B.$r^2$
- C.$\dfrac{1}{r}$
- D.$\dfrac{1}{r^2}$
2.
The acceleration due to gravity near Earth is about:
- A.$1.6\ \text{m/s}^2$
- B.$9.8\ \text{m/s}^2$
- C.$98\ \text{m/s}^2$
- D.$0\ \text{m/s}^2$
3.
Which is constant everywhere in the universe?
- A.weight
- B.mass
- C.value of $g$
- D.buoyant force
4.
The SI unit of pressure is the:
- A.newton
- B.pascal
- C.joule
- D.watt
5.
Archimedes' upthrust equals the weight of the:
- A.body
- B.fluid displaced
- C.container
- D.air above
6.
An object floats when its density is ___ the fluid's:
- A.greater than
- B.less than
- C.exactly twice
- D.unrelated to
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
7.
State the universal law of gravitation.
8.
Give two differences between mass and weight.
9.
Define pressure and state its SI unit.
10.
State Archimedes' principle.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
11.
A stone is dropped from a $125\ \text{m}$ cliff. Find the time to reach the ground and its final speed.
12.
A body of mass $300\ \text{g}$ has volume $150\ \text{cm}^3$. Find its density and relative density.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
13.
Derive $g = \dfrac{GM}{R^2}$ and explain how $g$ changes with altitude and at the poles versus the equator.
14.
An object weighs $50\ \text{N}$ in air and $40\ \text{N}$ in water. Find the buoyant force, the volume of the object, and explain whether it would float if released. (Use $g = 10\ \text{m/s}^2$.)
Answer Key
Section A — Multiple Choice Questions
- (D) $\dfrac{1}{r^2}$
- (B) $9.8\ \text{m/s}^2$
- (B) mass
- (B) pascal
- (B) fluid displaced
- (B) less than
Section B — Short Answer (2 marks)
- Every object attracts every other with force $F = \dfrac{G m_1 m_2}{r^2}$, proportional to the product of masses and inversely proportional to the square of the distance.
- Mass (kg, scalar, constant) is the amount of matter; weight (N, vector, varies with $g$) is the force of gravity, $W = mg$.
- Pressure is force per unit area, $P = \dfrac{F}{A}$; SI unit pascal ($\text{N/m}^2$).
- A body immersed in a fluid experiences an upward buoyant force equal to the weight of fluid it displaces.
Section C — Short Answer (3 marks)
- $h = \tfrac12 g t^2 \Rightarrow 125 = 5t^2 \Rightarrow t = 5\ \text{s}$; $v = gt = 10 \times 5 = 50\ \text{m/s}$.
- $\rho = \dfrac{300}{150} = 2\ \text{g/cm}^3 = 2000\ \text{kg/m}^3$; R.D. $= 2$.
Section D — Long Answer (5 marks)
- From $mg = \dfrac{GMm}{R^2}$, cancel $m$ to get $g = \dfrac{GM}{R^2}$. $g$ decreases with altitude as $r$ grows; it is greatest at the poles (smallest $R$) and least at the equator (largest $R$).
- Buoyant force $= 50 - 40 = 10\ \text{N}$. Upthrust $= \rho_w V g \Rightarrow 10 = 1000 \times V \times 10 \Rightarrow V = 10^{-3}\ \text{m}^3 = 1000\ \text{cm}^3$. Its weight ($50\ \text{N}$) exceeds the maximum upthrust ($10\ \text{N}$), so its density is greater than water's and it sinks.
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