The position of an object having mass 0.1 kg as a function of time t is given as

Question

The position of an object having mass 0.1 kg as a function of time $t$ is given as $\vec{r} = (10 t^{2} \hat{i} + 5 t^{3} \hat{j}) m .$

At $t = 1 s$ , which of the following statements are correct?

A. The linear momentum $\vec{p} = (2 \hat{i} + 1.5 \hat{j}) kg \cdot m / s .$

B. The force acting on the object $\vec{F} = (2 \hat{i} + 3 \hat{j}) N .$

C. The angular momentum of the object about its origin $\vec{L} = 15 \hat{k} J s .$

D. The torque acting on the object about its origin $\vec{τ} = 20 \hat{k} N m .$

Choose the correct answer from the option given below. [2026]

Smart Achievers · Accepted Answer

(4)

$Given \vec{r} = 10 t^{2} \hat{i} + 5 t^{3} \hat{j} \Rightarrow {\vec{r}}_{t = 1 s} = (10 \hat{i} + 5 \hat{j}) m$

$\vec{v} = \frac{d \vec{r}}{d t} = 20 t \hat{i} + 15 t^{2} \hat{j} \Rightarrow {\vec{v}}_{t = 1 \sec} = (20 \hat{i} + 15 \hat{j}) m / s$

$\vec{a} = \frac{d^{2} \vec{r}}{d t^{2}} = 20 \hat{i} + 30 t \hat{j} \Rightarrow {\vec{a}}_{t = 1 \sec} = (20 \hat{i} + 30 \hat{j}) m / s^{2}$

$\vec{p} = m \vec{v} = 0.1 (20 \hat{i} + 15 \hat{j}) = (2 \hat{i} + 1.5 \hat{j}) kg \cdot m / s$

$\vec{F} = m \vec{a} = (2 \hat{i} + 3 \hat{j}) N$

$\vec{L} = (10 \hat{i} + 5 \hat{j}) \times (2 \hat{i} + 1.5 \hat{j}) = 15 \hat{k} - 10 \hat{k} = 5 \hat{k} Js$

$\vec{τ} = \vec{r} \times \vec{F} = (10 \hat{i} + 5 \hat{j}) \times (2 \hat{i} + 3 \hat{j}) = 20 \hat{k} Nm$

$A, B & D are correct$

Want Us to Email you About Special Offers & Updates?