Motion In One Dimension JEE Advanced previous year questions with solutions

1 solved JEE Advanced questions on Motion In One Dimension, free to read — no sign-in needed. The full chapter has 4 questions; sign in to attempt the remaining 3 in the exam simulator.

1. Q1JEE Advanced Adv 2016 (Paper 1)
   The positon vector $\vec{r}$ of a particle of mass m is given by the following equation $\vec{r}\left(t\right)=\alpha {t}^{3}\hat{i}+\beta {t}^{2}\hat{j},where\alpha =\dfrac{10}{3}m{s}^{-3},\beta =5m{s}^{-2}andm=0.1kg.Att=1s,$ which of the following statements (s) is (are) true about the particle?
   1. A.The velocity $\vec{v}$ is given by $\vec{v}=\left(10\hat{i}+10\hat{j}\right)m{s}^{-1}$
   2. B.The angular momentum $\vec{L}$ with respect to the origin is given by $\vec{L}=-\left(\dfrac{5}{3}\right)\hat{k}Nms$
   3. C.The force $\vec{F}$ is given by $\vec{F}=\left(\hat{i}+2\hat{j}\right)N$
   4. D.The torque $\vec{\tau }$ with respect to the origin is given by $\vec{\tau }=-\left(\dfrac{20}{3}\right)\hat{k}Nm$
   Show answer & solution

   Answer: A,B,D

   $\vec{r}=\alpha {t}^{3}\hat{i}+\beta {t}^{2}\hat{j}$ $\vec{v}=\dfrac{d\vec{r}}{dt}=3\alpha {t}^{2}\hat{i}+2\beta t\hat{j}$ $\vec{a}=\dfrac{{d}^{2}\vec{r}}{d{t}^{2}}=6\alpha t\hat{i}+2\beta \hat{j}$ At t = 1 (i) $\vec{v}=3\times \dfrac{10}{3}\times 1\hat{i}+2\times J\times 1\hat{j}$ $=10\hat{i}+10\hat{j}$ (ii) $\vec{L}=\vec{r}\times \vec{p}$ $=\left(\dfrac{10}{3}\times 1\hat{i}+5\times 1\hat{j}\right)\times 0.1\left(10\hat{i}+10\hat{j}\right)$ $=-\dfrac{5}{3}\hat{k}$ (iii) $\vec{F}=m\times \left(6\times \dfrac{10}{3}\times 1\hat{i}+2\times 5\hat{j}\right)=2\hat{i}+\hat{j}$ (iv) $\vec{\tau }=r\times \vec{F}$ $=\left(\dfrac{10}{3}\hat{i}+5\hat{j}\right)\times \left(2\hat{i}+\hat{j}\right)$ $=+\dfrac{10}{3}\hat{k}+10\left(-\hat{k}\right)$ $=-\dfrac{20}{3}\hat{k}$