A) \[{{90}^{\text{o}}}\]
B) \[{{0}^{\text{o}}}\]
C) \[{{180}^{\text{o}}}\]
D) \[{{30}^{\text{o}}}\]
Correct Answer: A
Solution :
\[{{p}_{x}}=2\cos t,\,\,{{p}_{y}}=2\sin t\] \[\therefore \] \[p={{p}_{x}}\,\,i+{{p}_{y}}\,\,j\] \[=2\cos t\,\,i+2\sin t\,\,j\] Force = rate of change of momentum \[=\frac{d\,\,p}{dt}\] \[\Rightarrow \] \[F=-2\sin t\,\,i+2\cos t\,\,j\] \[\therefore \] \[\cos \theta =\frac{F\cdot p}{\left| F \right|\cdot \left| p \right|}\] \[=\frac{(-2\sin t\,\,i+2\cos t\,\,j)(2\cos t\,\,i+2\sin t\,\,j)}{\sqrt{4{{\sin }^{2}}t+4{{\cos }^{2}}t}\sqrt{4{{\cos }^{2}}t+4{{\sin }^{2}}t}}\] \[\Rightarrow \] \[\cos \theta =0\] \[\Rightarrow \] \[\theta ={{90}^{o}}\]
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