What is the SI unit of momentum? | Mathematics MCQ

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What is the SI unit of momentum?

$\text{kg m}^{-1} \text{s}^{-1}$

$\text{kg m s}$

$\text{kg m s}^{-1}$

$\text{kg m}$

Correct Answer

📐 MA • Math Area Ratio TheoremMathematicsPrevious Year Paper 2024

Option C

$\text{kg m s}^{-1}$

Quick Summary:

Ratio of areas of two similar triangles equals the square of the ratio of their corresponding sides: $\text{Area Ratio} = 1^2: 3^2 = 1: 9$ . Therefore, $\text{Area}(\Delta PQR) = 9 \times 25 = 225\text{ cm}^2$ .

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📐MAMath SolutionArea Ratio Theorem

📋 Given

Two similar triangles $\Delta ABC \sim \Delta PQR$ with side ratio $\frac{AB}{PQ} = \frac{1}{3}$ . Area of $\Delta ABC = 25\text{ cm}^2$ .

🔢 Formula Used

Area(ΔABC)Area(ΔPQR)=(ABPQ)2\frac{\text{Area}(\Delta ABC)}{\text{Area}(\Delta PQR)} = \left(\frac{AB}{PQ}\right)^2Area(ΔPQR)Area(ΔABC)​=(PQAB​)2

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Taking the linear ratio instead of squaring it, i.e., incorrectly computing $\text{Area}(\Delta PQR) = 3 \times 25 = 75\text{ cm}^2$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Recall the Area Ratio Theorem for Similar Triangles

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Area(ΔABC)Area(ΔPQR)=(ABPQ)2\frac{\text{Area}(\Delta ABC)}{\text{Area}(\Delta PQR)} = \left(\frac{AB}{PQ}\right)^2Area(ΔPQR)Area(ΔABC)​=(PQAB​)2

Substitute the Given Values

We are given that $\frac{AB}{PQ} = \frac{1}{3}$ and $\text{Area}(\Delta ABC) = 25\text{ cm}^2$ . Substitute these into the formula:

25Area(ΔPQR)=(13)2=19\frac{25}{\text{Area}(\Delta PQR)} = \left(\frac{1}{3}\right)^2 = \frac{1}{9}Area(ΔPQR)25​=(31​)2=91​

Calculate the Area of $\Delta PQR$

Cross-multiplying to solve for $\text{Area}(\Delta PQR)$ :

Area(ΔPQR)=25×9=225 cm2\text{Area}(\Delta PQR) = 25 \times 9 = 225\text{ cm}^2Area(ΔPQR)=25×9=225 cm2

✅

C is correct because the area of $\Delta PQR$ is calculated as $25 \times 3^2 = 225\text{ cm}^2$ .

Core Concepts Used

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💡 EXAM TIP

For 2D similar figures, areas scale by the square of the linear scale factor ( $k^2$ ). For 3D similar solids, volumes scale by the cube of the linear scale factor ( $k^3$ ).

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