Duration: 10:51

23 views

0

The position vector \( \overrightarrow{\mathrm{r}} \) of a particle of mass \( \mathrm{m} \) is given by the following equation
\[
\vec{r}(t)=\alpha t^{3} \hat{i}+\beta t^{2} \hat{j},
\]
where \( \alpha=10 / 3 \mathrm{~ms}^{-3}, \beta=5 \mathrm{~ms}^{-2} \) and \( \mathrm{m}=0.1 \mathrm{~kg} \). At \( \mathrm{t}=1 \mathrm{~s} \), which of the following statement(s) is (are) true about the particle?
(A) The velocity \( \overrightarrow{\mathrm{v}} \) is given by \( \overrightarrow{\mathrm{v}}=(10 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{ms}^{-1} \)
(B) The angular momentum \( \overrightarrow{\mathrm{L}} \) with respect to the origin is given by \( \overrightarrow{\mathrm{L}}=-(5 / 3) \hat{\mathrm{k}} \mathrm{N} \mathrm{ms} \)
(C) The force \( \overrightarrow{\mathrm{F}} \) is given by \( \overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}) \mathrm{N} \)
(D) The torque \( \vec{\tau} \) with respect to the origin is given by \( \vec{\tau}=-(20 / 3) \hat{\mathrm{k}} \mathrm{N} \mathrm{m} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live