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(D) Given position vector $\vec{r} = 10t^2\hat{i} + 5t^3\hat{j}$.Velocity $\vec{v} = \frac{d\vec{r}}{dt} = 20t\hat{i} + 15t^2\hat{j}$.At $t = 1 	ext{

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$A, B$ and $D$ only

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(D) Given position vector $\vec{r} = 10t^2\hat{i} + 5t^3\hat{j}$.Velocity $\vec{v} = \frac{d\vec{r}}{dt} = 20t\hat{i} + 15t^2\hat{j}$.At $t = 1 	ext{ s}$,$\vec{v} = 20\hat{i} + 15\hat{j} 	ext{ m/s}$.Linear momentum $\vec{p} = m\vec{v} = 0.1(20\hat{i} + 15\hat{j}) = (2\hat{i} + 1.5\hat{j}) 	ext{ kg} \cdot 	ext{m/s}$. Thus,statement $A$ is correct.Acceleration $\vec{a} = \frac{d\vec{v}}{dt} = 20\hat{i} + 30t\hat{j}$.At $t = 1 	ext{ s}$,$\vec{a} = 20\hat{i} + 30\hat{j} 	ext{ m/s}^2$.Force $\vec{F} = m\vec{a} = 0.1(20\hat{i} + 30\hat{j}) = (2\hat{i} + 3\hat{j}) 	ext{ N}$. Thus,statement $B$ is correct.At $t = 1 	ext{ s}$,$\vec{r} = 10(1)^2\hat{i} + 5(1)^3\hat{j} = 10\hat{i} + 5\hat{j}$.Angular momentum $\vec{L} = \vec{r} 	imes \vec{p} = (10\hat{i} + 5\hat{j}) 	imes (2\hat{i} + 1.5\hat{j}) = (15\hat{k} - 10\hat{k}) = 5\hat{k} 	ext{ J} \cdot 	ext{s}$. Thus,statement $C$ is incorrect.Torque $\vec{	au} = \vec{r} 	imes \vec{F} = (10\hat{i} + 5\hat{j}) 	imes (2\hat{i} + 3\hat{j}) = (30\hat{k} - 10\hat{k}) = 20\hat{k} 	ext{ N} \cdot 	ext{m}$. Thus,statement $D$ is correct.Therefore,statements $A, B$ and $D$ are correct.

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