JEE Main 2026 — Apr 2, Shift 1 — Physics solution

JEE Main2026Apr 2, Shift 1Physics

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

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

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

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

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

Choose the correct answer from the option given below.

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

Solution

Given $r = 10 t^{2} \hat{i} + 5 t^{3} \hat{j}$ . Taking successive time derivatives:

$v = 20 t \hat{i} + 15 t^{2} \hat{j}, a = 20 \hat{i} + 30 t \hat{j}$

Evaluating at $t = 1$ s with $m = 0.1$ kg:

$r = 10 \hat{i} + 5 \hat{j}, v = 20 \hat{i} + 15 \hat{j}, a = 20 \hat{i} + 30 \hat{j}$

$p = m v = 2 \hat{i} + 1.5 \hat{j}$ kg $\cdot$ m/s $\Rightarrow$ A correct.

$F = m a = 2 \hat{i} + 3 \hat{j}$ N $\Rightarrow$ B correct.

$τ = r \times F = (10 \hat{i} + 5 \hat{j}) \times (2 \hat{i} + 3 \hat{j}) = (30 - 10) \hat{k} = 20 \hat{k}$ Nm $\Rightarrow$ D correct.

$L = r \times p = (10 \hat{i} + 5 \hat{j}) \times (2 \hat{i} + 1.5 \hat{j}) = (15 - 10) \hat{k} = 5 \hat{k}$ Js (not $15 \hat{k}$ ) $\Rightarrow$ C incorrect.

Hence A, B and D are correct.

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