The position of an object… - JEE Main 2026 Physics PYQ

JEE Main 2026 — Physics Mechanics

2026mcqmedium

The position of an object having mass $0.1$ kg as a function of time $t$ is given as $\vec{r} = \left(10t^2\hat{i} + 5t^3\hat{j}\right)$ m. At $t = 1$ s, which of the following statements are correct?

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

B. The force acting on the object $\vec{F} = \left(2\hat{i} + 3\hat{j}\right)$ 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 $\vec{\tau} = 20\hat{k}$ N·m.

Choose the correct answer from the options given below :

Official previous-year question

Held on 2 Apr 2026 · Verified 6 Jul 2026.

Options

A
A, B and C only
B
B, C and D only
C
A, C and D only
D
A, B and D only

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Solution

Given the position vector $\vec{r} = 10t^2\hat{i} + 5t^3\hat{j}$

Velocity $\vec{v} = \dfrac{d\vec{r}}{dt} = 20t\hat{i} + 15t^2\hat{j}$

Acceleration $\vec{a} = \dfrac{d\vec{v}}{dt} = 20\hat{i} + 30t\hat{j}$

At $t = 1$ s:

$\vec{r} = 10\hat{i} + 5\hat{j}$ m

$\vec{v} = 20\hat{i} + 15\hat{j}$ m/s

$\vec{a} = 20\hat{i} + 30\hat{j}$ m/s $^2$

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

Force $\vec{F} = m\vec{a} = 0.1(20\hat{i} + 30\hat{j}) = 2\hat{i} + 3\hat{j}$ N (Statement B is correct)

Angular momentum $\vec{L} = \vec{r} \times \vec{p} = (10\hat{i} + 5\hat{j}) \times (2\hat{i} + 1.5\hat{j}) = (10 \times 1.5 - 5 \times 2)\hat{k} = 5\hat{k}$ J $\cdot$ s (Statement C is incorrect)

Torque $\vec{\tau} = \vec{r} \times \vec{F} = (10\hat{i} + 5\hat{j}) \times (2\hat{i} + 3\hat{j}) = (10 \times 3 - 5 \times 2)\hat{k} = 20\hat{k}$ N $\cdot$ m (Statement D is correct)

Therefore, statements A, B, and D are correct.

Answer: A, B and D only

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Solution

Given the position vector $\vec{r} = 10t^2\hat{i} + 5t^3\hat{j}$

Velocity $\vec{v} = \dfrac{d\vec{r}}{dt} = 20t\hat{i} + 15t^2\hat{j}$

Acceleration $\vec{a} = \dfrac{d\vec{v}}{dt} = 20\hat{i} + 30t\hat{j}$

At $t = 1$ s:

$\vec{r} = 10\hat{i} + 5\hat{j}$ m

$\vec{v} = 20\hat{i} + 15\hat{j}$ m/s

$\vec{a} = 20\hat{i} + 30\hat{j}$ m/s $^2$

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

Force $\vec{F} = m\vec{a} = 0.1(20\hat{i} + 30\hat{j}) = 2\hat{i} + 3\hat{j}$ N (Statement B is correct)

Angular momentum $\vec{L} = \vec{r} \times \vec{p} = (10\hat{i} + 5\hat{j}) \times (2\hat{i} + 1.5\hat{j}) = (10 \times 1.5 - 5 \times 2)\hat{k} = 5\hat{k}$ J $\cdot$ s (Statement C is incorrect)

Torque $\vec{\tau} = \vec{r} \times \vec{F} = (10\hat{i} + 5\hat{j}) \times (2\hat{i} + 3\hat{j}) = (10 \times 3 - 5 \times 2)\hat{k} = 20\hat{k}$ N $\cdot$ m (Statement D is correct)

Therefore, statements A, B, and D are correct.

Answer: A, B and D only

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Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics