A particle is pushed by forces 2 i +3 j -2 k and 5 i + j -2 k sim… - Vidyadip

MCQ

A particle is pushed by forces $2\hat{\text{i}}+3\hat{\text{j}}-2\hat{\text{k}}$ and $5\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$ simultaneously and it is displaced from point $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ to point $2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}}$. The work done is:

A
$7$ units.
✓
$-7$ units.
C
$10$ units.
D
$-10$ units.

✓

Answer

Correct option: B.

$-7$ units.

Net force, $=2\hat{\text{i}}+3\hat{\text{j}}-2\hat{\text{k}+}5\hat{\text{i}}-\hat{\text{j}}-3\hat{\text{k}}$
$=7\hat{\text{i}}+2\hat{\text{j}}-5\hat{\text{k}}$
Diolacement, $\text{d}=2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}-}\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}}$
$=\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}}$
Work done $=\text{F}.\text{d}=(7\hat{\text{i}}+2\hat{\text{j}}-5\hat{\text{k}}).(\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}})$
$=7-4-10$
$=-7\text{ units}$.

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