JEE Mains · Physics · STD 11 - Motion in plane
- JEE Mains 2020
- Medium
- MCQ
A particle moves such that its position vector \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\overrightarrow{\mathrm{v}}(\mathrm{t})\) and acceleration \(\overrightarrow{\mathrm{a}}(\mathrm{t})\) of the particle
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\overrightarrow{\mathrm{v}}\) is perpendicular to \(\overrightarrow{\mathrm{r}}\) and \(\overrightarrow{\mathrm{a}}\) is directed towards the origin
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}\)
On diff. we get
\({\overrightarrow{\mathrm{v}}=-\omega \sin \omega \mathrm{t} \hat{\mathrm{i}}+\omega \cos \omega \mathrm{t} \hat{\mathrm{j}}}\)
\({\overrightarrow{\mathrm{a}}=-\omega^{2} \overrightarrow{\mathrm{r}}}\)
\({\overrightarrow{\mathrm{v}} \cdot \overrightarrow{\mathrm{r}}=0}\)
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