A) \[\sqrt{45}\]
B) \[45\]
C) \[24\]
D) \[\sqrt{24}\]
Correct Answer: C
Solution :
Key Idea: Power developed is equal to scalar product of force and velocity vector. Power is given by \[P=\overset{\to }{\mathop{\mathbf{F}}}\,\cdot \overset{\to }{\mathop{\mathbf{v}}}\,\] Given, \[\overset{\to }{\mathop{\mathbf{F}}}\,=7\widehat{\mathbf{i}}+6\widehat{\mathbf{k}},\,\,\overset{\to }{\mathop{\mathbf{v}}}\,=3\widehat{\mathbf{j}}+4\widehat{\mathbf{k}}\] \[\therefore \] \[P=\overset{\to }{\mathop{\mathbf{F}}}\,\cdot \overset{\to }{\mathop{\mathbf{v}}}\,\] \[P=(7\widehat{\mathbf{i}}+6\widehat{\mathbf{k}})\cdot (3\widehat{\mathbf{i}}+4\widehat{\mathbf{k}})\] \[P=6\times 4\] \[P=24\,\,unit\] Note: Power is a scalar quantity.
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