A body constrained to move along y- axis is subjected to a consta… - Vidyadip

MCQ

A body constrained to move along $y-$ axis is subjected to a constant force $\vec F = -\hat i + 2\hat j+ 3\hat k\,\,N$ . The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$

A
$4$
✓
$8$
C
$12$
D
$24$

✓

Answer

Correct option: B.

$8$

b
Here, $\overrightarrow{\mathrm{F}}=(-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \mathrm{N}$

As the body moves a distance of $4 \mathrm{m}$ along

$\mathrm{y}$ $-axis,$

$\therefore \overrightarrow{\mathrm{d}}=4 \hat{j} \mathrm{m}$

Work doen by the given force is

$\mathrm{W}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{d}}=(-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \mathrm{N}) \cdot(4 \hat{\mathrm{j}} \mathrm{m})=8 \mathrm{J}$

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