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

The correct answer is Option 4. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q28 – JEE-MAIN 2026

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Home Physics Laws of MotionQuestion #213

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

is _______.

Clue 1 of 3: Fundamental Laws of Motion

Recall Newton's second law to find the acceleration of the body and the kinematic equation for position.

🧠 Full Solution Path

Step 1: Calculate the acceleration of the body✦ Active

First, convert the mass to kilograms and then use Newton's second law, $\vec{F} = m \vec{a}$ , to find the acceleration vector.

m = 100 g = 0.1 kg

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

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

Step 2: Determine the final position of the body○ Expand

Assuming the body starts from rest at the origin (initial position ${\vec{r}}_{0} = 0$ and initial velocity ${\vec{v}}_{0} = 0$ ), use the kinematic equation for position at time $t = 2 s$ .

\vec{r} = {\vec{r}}_{0} + {\vec{v}}_{0} t + \frac{1}{2} \vec{a} t^{2}

\vec{r} = 0 + 0 \cdot (2) + \frac{1}{2} (50 \hat{i} + 100 \hat{j}) (2)^{2}

\vec{r} = \frac{1}{2} (50 \hat{i} + 100 \hat{j}) (4) = (100 \hat{i} + 200 \hat{j}) m

Step 3: Equate components and find the ratio

x : y

○ Expand

The calculated final position is $(100 \hat{i} + 200 \hat{j}) m$ . This is given as $(2 x \hat{i} + 5 y \hat{j}) m$ . Equate the corresponding components to solve for $x$ and $y$ , then find their ratio.

(2 x \hat{i} + 5 y \hat{j}) = (100 \hat{i} + 200 \hat{j})

2 x = 100 ⟹ x = 50

5 y = 200 ⟹ y = 40

x : y = 50 : 40 = 5 : 4

💡 Teacher's Secret Hint

Ensure units are consistent (SI units) before performing calculations.

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Physics Question 28 – JEE-MAIN 2026

Clue 1 of 3: Fundamental Laws of Motion

🧠 Full Solution Path