JEE Main 2026 — Apr 4, Shift 2 — Physics solution

JEE Main2026Apr 4, Shift 2Physics

At $t = 0$ , a body of mass 100 g starts moving under the influence of a force $(5 \hat{i} + 10 \hat{j}) N$ . After 2s its position is $(2 x \hat{i} + 5 y \hat{j}) m$ . The ratio $x : y$ is ______.

A
1 : 2
B
2 : 5
C
5 : 2
D
5 : 4

Solution

Mass $m = 0.1$ kg. Acceleration:

$a = \frac{F}{m} = \frac{5 i ^ + 10 j ^}{0.1} = 50 \hat{i} + 100 \hat{j} m/s^{2}$ .

Starting from rest, displacement after 2s is $s = \frac{1}{2} a t^{2} = \frac{1}{2} (50 \hat{i} + 100 \hat{j}) (4) = 100 \hat{i} + 200 \hat{j} m$ .

Matching components with $2 x \hat{i} + 5 y \hat{j}$ : $2 x = 100 \Rightarrow x = 50$ and $5 y = 200 \Rightarrow y = 100$ .

$∴ \frac{x}{y} = \frac{50}{100} = \frac{5}{4}$ , i.e. $x : y = 5 : 4$ .

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