Grade 9 : Social Science - 2. Shaping Earth (Set 1) | Concept of Maths

Question 1

1. The Earth's crust is divided into several tectonic plates. If the Pacific Plate moves at an average rate of $r = 7\text{ cm}$ per year, how many meters will it displace in $t = 250$ years?

A) $1.75\text{ m}$

B) $14.5\text{ m}$

C) $17.5\text{ m}$

D) $175\text{ m}$

Answer

Correct Answer: C

To find the total displacement $D$, we use the formula: $$D = r \times t$$ Given $r = 7\text{ cm/year}$ and $t = 250\text{ years}$: $$D = 7 \times 250 = 1750\text{ cm}$$ Since $100\text{ cm} = 1\text{ meter}$, we convert: $$D = \frac{1750}{100} = 17.5\text{ meters}.$$ Correct Answer: 17.5 m.

Question 2

2. The radius of the Earth is approximately $R \approx 6371\text{ km}$. If the average thickness of the continental crust is $d = 35\text{ km}$, what percentage of the Earth's radius does the crust represent?

A) $\approx 0.55\%$

B) $\approx 1.55\%$

C) $\approx 5.50\%$

D) $\approx 0.05\%$

Answer

Correct Answer: A

Percentage is calculated as: $$\text{Percentage} = \left( \frac{d}{R} \right) \times 100$$ $$\text{Percentage} = \left( \frac{35}{6371} \right) \times 100 \approx 0.005493 \times 100 \approx 0.55\%.$$ This demonstrates how thin the crust is compared to the rest of the Earth.

Question 3

3. Earthquake energy increases significantly with magnitude. Each whole number increase on the Richter scale represents approximately $32$ times more energy release. How much more energy is released by a magnitude $M = 8$ earthquake compared to a magnitude $M = 5$?

A) $96$ times

B) $1,024$ times

C) $3,200$ times

D) $32,768$ times

Question 4

4. The temperature inside the Earth increases with depth. If the geothermal gradient is approximately $25^{\circ}\text{C}$ per km and the surface temperature is $20^{\circ}\text{C}$, what is the estimated temperature at a depth of $4.5\text{ km}$?

A) $112.5^{\circ}\text{C}$

B) $132.5^{\circ}\text{C}$

C) $145.0^{\circ}\text{C}$

D) $152.5^{\circ}\text{C}$

Answer

Correct Answer: B

Let $T_s$ be surface temp, $g$ be gradient, and $d$ be depth. $$T_d = T_s + (g \times d)$$ $$T_d = 20 + (25 \times 4.5)$$ $$T_d = 20 + 112.5 = 132.5^{\circ}\text{C}.$$

Question 5

5. Due to the collision of the Indian and Eurasian plates, the Himalayas are rising. If the rate of uplift is $5\text{ mm}$ per year, how many centimeters will the range rise in $1,200$ years?

A) $60\text{ cm}$

B) $600\text{ cm}$

C) $6,000\text{ cm}$

D) $6\text{ cm}$

Answer

Correct Answer: B

Total uplift in mm: $$5\text{ mm/yr} \times 1200\text{ yrs} = 6000\text{ mm}$$ Convert to cm: $$10\text{ mm} = 1\text{ cm} \implies \frac{6000}{10} = 600\text{ cm}.$$

Question 6

6. Physical weathering can break rocks through thermal expansion. If a rock segment of length $L = 20\text{ m}$ expands by a factor of $\alpha = 0.0001$ per degree Celsius, what is the expansion $\Delta L$ in millimeters when the temperature rises by $40^{\circ}\text{C}$?

A) $0.8\text{ mm}$

B) $80\text{ mm}$

C) $80.0\text{ mm}$

D) $8\text{ mm}$

Answer

Correct Answer: C

Expansion formula: $$\Delta L = L \times \alpha \times \Delta T$$ $$\Delta L = 20 \times 0.0001 \times 40$$ $$\Delta L = 0.08\text{ meters}$$ Convert to mm: $0.08 \times 1000 = 80\text{ mm}$. (Self-correction: Option C is $80$ mm).

Question 7

7. In a symmetric V-shaped river valley, the slopes make an angle of $45^{\circ}$ with the horizontal. If the valley is $100\text{ m}$ deep, what is the total horizontal width from one rim to the other? (Hint: $\tan(45^{\circ}) = 1$)

A) $200\text{ m}$

B) $100\text{ m}$

C) $141\text{ m}$

D) $50\text{ m}$

Answer

Correct Answer: A

For a $45^{\circ}$ angle, the depth ($h$) equals the horizontal distance from the center to the rim ($w_c$). $$w_c = h \times \cot(45^{\circ}) = 100 \times 1 = 100\text{ m}$$ Total width $W$ is twice the distance from center to rim: $$W = 2 \times 100 = 200\text{ m}.$$

Question 8

8. It takes roughly $400$ years to form just $1\text{ cm}$ of topsoil through natural weathering. How many centuries would it take to form a layer of soil $15\text{ cm}$ thick?

A) $15$ centuries

B) $40$ centuries

C) $60$ centuries

D) $6,000$ centuries

Answer

Correct Answer: C

Total years required: $$15\text{ cm} \times 400\text{ years/cm} = 6000\text{ years}$$ Since $1\text{ century} = 100\text{ years}$: $$\frac{6000}{100} = 60\text{ centuries}.$$

Question 9

9. Pangea started breaking up about $200$ million years ago. If the Atlantic Ocean is now $5000\text{ km}$ wide, what is the average annual spreading rate in cm/year?

A) $25\text{ cm/yr}$

B) $0.25\text{ cm/yr}$

C) $250\text{ cm/yr}$

D) $2.5\text{ cm/yr}$

Answer

Correct Answer: D

Convert distance to cm: $$5000\text{ km} = 5,000,000\text{ meters} = 500,000,000\text{ cm}$$ Time $T = 200,000,000\text{ years}$. Rate $r = D/T$: $$r = \frac{500,000,000}{200,000,000} = \frac{5}{2} = 2.5\text{ cm/year}.$$

Question 10

10. Earth's internal structure consists of the Crust ($35\text{ km}$), Mantle ($2900\text{ km}$), and the Core. Given the radius of Earth is $6371\text{ km}$, what is the radius of the Core?

A) $3271\text{ km}$

B) $3436\text{ km}$

C) $3471\text{ km}$

D) $2900\text{ km}$

Answer

Correct Answer: B

The radius of the Core is the total radius minus the thickness of the Crust and Mantle. $$R_{core} = R_{earth} - (d_{crust} + d_{mantle})$$ $$R_{core} = 6371 - (35 + 2900)$$ $$R_{core} = 6371 - 2935 = 3436\text{ km}.$$

Accepted Answer

Correct Answer: D

The difference in magnitude is $\Delta M = 8 - 5 = 3$. If each step is a factor of $32$, the total factor $F$ is: $$F = 32^3 = 32 \times 32 \times 32 = 32,768$$ An earthquake of magnitude 8 is roughly $32,768$ times more powerful than one of magnitude 5.

Grade 9 : Social Science - 2. Shaping Earth (Set 1) | Concept of Maths