Question:
A 15 W machine used $(3i + 5j + 6k)$ N force for 6 seconds to lift a body through a distance of X m along x - axis. The value of X is:
A 15 W machine used $(3i + 5j + 6k)$ N force for 6 seconds to lift a body through a distance of X m along x - axis. The value of X is:
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Work = Force dot Displacement; Power = Work / Time.
Updated On: Jun 6, 2026
- 20m
- 25m
- 30m
- 35m
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The Correct Option is C
Solution and Explanation
Step 1: Relations used.
Power is work per unit time, $P = \dfrac{W}{t}$, and work is $W = \vec{F}\cdot\vec{S}$.
Step 2: Work in terms of X.
The body moves only along the x-axis, so $\vec{S} = X\hat{i}$ and $W = (3\hat{i}+5\hat{j}+6\hat{k})\cdot(X\hat{i}) = 3X$ J.
Step 3: Total work from power.
$W = P t = 15 \times 6 = 90$ J.
Step 4: Solve.
$3X = 90 \Rightarrow X = 30$ m. \[ \boxed{30\ \text{m}} \]
Power is work per unit time, $P = \dfrac{W}{t}$, and work is $W = \vec{F}\cdot\vec{S}$.
Step 2: Work in terms of X.
The body moves only along the x-axis, so $\vec{S} = X\hat{i}$ and $W = (3\hat{i}+5\hat{j}+6\hat{k})\cdot(X\hat{i}) = 3X$ J.
Step 3: Total work from power.
$W = P t = 15 \times 6 = 90$ J.
Step 4: Solve.
$3X = 90 \Rightarrow X = 30$ m. \[ \boxed{30\ \text{m}} \]
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