A) \[100\,\,\text{J}\]
B) \[50\,\,\text{J}\]
C) \[200\,\,\text{J}\]
D) \[75\,\,\text{J}\]
Correct Answer: A
Solution :
Using the formula for work done \[W=\overset{\to }{\mathop{\mathbf{F}}}\,\cdot \overset{\to }{\mathop{\mathbf{r}}}\,=\overset{\to }{\mathop{\mathbf{F}}}\,\cdot (\overset{\to }{\mathop{{{\mathbf{r}}_{2}}}}\,-\overset{\to }{\mathop{{{\mathbf{r}}_{1}}}}\,)\] \[W=(4\mathbf{\hat{i}}+\mathbf{\hat{j}}+3\mathbf{\hat{k}})\cdot (14\mathbf{\hat{i}}+13\mathbf{\hat{j}}+9\mathbf{\hat{k}}\] \[-3\mathbf{\hat{i}}-2\mathbf{\hat{j}}+6\mathbf{\hat{k}})\] \[W=(4\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\cdot (11\widehat{\mathbf{i}}+11\widehat{\mathbf{j}}+15\widehat{\mathbf{k}})\] \[W=44+11+45=100\,\,joule\]You need to login to perform this action.
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