JEE PYQ: Units & Measurements - Question ID b8bb785fce14 (JEE Main 2008)

Core Formula & Concept:

In classical mechanics, the momentum of a body is defined as the product of its mass and its velocity. Mathematically, this is expressed as:

$\vec{p} = m \vec{v}$

where:

• $\vec{p}$ is the momentum vector,
• $m$ is the mass of the body, and
• $\vec{v}$ is the velocity vector.

Since the motion is along the x-axis, the magnitude of the momentum simplifies to: $p = m \cdot v$ where $v$ is the speed (magnitude of velocity).

The key concept here is significant figures. The number of significant figures in the final result must match the least number of significant figures in the given data (mass and speed).

Step-by-Step Derivation:

Step 1: Identify given values
Mass, $m = 3.513 \, \text{kg}$ (4 significant figures)
Speed, $v = 5.00 \, \text{ms}^{-1}$ (3 significant figures)

Step 2: Compute the product
$p = m \cdot v = 3.513 \times 5.00$

Step 3: Perform the multiplication
Multiply $3.513$ by $5.00$:

• $3.513 \times 5 = 17.565$

Since $5.00$ has 3 significant figures, the result must be rounded to 3 significant figures.

Step 4: Apply rounding rules
The computed value is $17.565$.
The digit after the third significant figure is $6$, which is $\geq 5$.
Thus, we round up the third digit ($5$) to $6$, giving: $p = 17.6 \, \text{kg ms}^{-1}$

Step 5: Match with given options
The rounded value $17.6 \, \text{kg ms}^{-1}$ corresponds to Option A.

Common Traps & Exam Tip:

Trap 1: Ignoring significant figures
Many students compute $3.513 \times 5.00 = 17.565$ and choose Option B without rounding. This is incorrect because the speed ($5.00$) has only 3 significant figures, so the final answer must also have 3 significant figures. Trap 2: Incorrect rounding
Some students round $17.565$ to $17.57$ (Option D) instead of $17.6$. This happens when they mistakenly consider the fourth digit ($5$) without proper rounding rules. Exam Tip:
Always check the number of significant figures in the given data. The final answer should match the least number of significant figures among the inputs. In this case, $5.00$ (3 sig figs) dictates the precision of the result.