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

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Laws of Motion

t = 0

, a body of mass 100 g starts moving under the influence of a force

(5 \hat{i} + 10 \hat{j}) N

. After 2 s its position is

(2 x \hat{i} + 5 y \hat{j}) m

. The ratio

x : y

____

(A) $1 : 2$
(B) $2 : 5$
(C) $5 : 2$
(D) $5 : 4$ ✓ Correct

Answer: (D)

Solution

The acceleration is

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

. Starting from rest,

s = \frac{1}{2} a t^{2} = \frac{1}{2} (50 \hat{i} + 100 \hat{j}) (2)^{2} = 100 \hat{i} + 200 \hat{j}

. Matching this to

2 x \hat{i} + 5 y \hat{j}

gives

x = 50

and

y = 40

, so

x : y = 50 : 40 = 5 : 4

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Single correct option

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