The displacement of a particle moving under the action of a force \(\vec{\mathrm{F}}=2\hat{\mathrm{i}}+\mathrm{b}\hat{\m…
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PYQThe displacement of a particle moving under the action of a force \(\vec{\mathrm{F}}=2\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}+\hat{\mathrm{k}}\) is \(\vec{\mathrm{d}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\). Find the value of \(b\) if the work done by the force is zero.
(Shift II Memory Based)
✓ Correct answer: c)
-3
Explanation
\(\mathrm{W}=\vec{\mathrm{F}}.\vec{\mathrm{d}}\\ 0=\left(\hat{2\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}+\hat{\mathrm{k}}\right).\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)\\ 0=2+\mathrm{b}+1\\ \mathrm{b}=-3\)
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