At , a body of mass 100 g starts moving under the influence of a force . After 2 s its position is . The ratio is

Question

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 2 s its position is $(2 x \hat{i} + 5 y \hat{j}) m$ . The ratio $x : y$ is _______. [2026]

Smart Achievers · Accepted Answer

(4)

$\vec{a} = \frac{\vec{F}}{m} = \frac{5 \hat{i} + 10 \hat{j}}{0.1} = (50 \hat{i} + 100 \hat{j})$

$\vec{s} = \vec{u} t + \frac{1}{2} \vec{a} t^{2}$

$\vec{s} = 0 + \frac{1}{2} [50 \hat{i} + 100 \hat{j}] {(2)}^{2}$

$\vec{s} = 100 \hat{i} + 200 \hat{j} = \vec{r} = 2 x \hat{i} + 5 y \hat{j}$

$2 x = 100 \Rightarrow x = 50 and 5 y = 200 \Rightarrow y = 40$

$\Rightarrow \frac{x}{y} = \frac{5}{4}$

Solution

Q.
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 2 s its position is $(2 x \hat{i} + 5 y \hat{j}) m$ . The ratio $x : y$ is _______. [2026]

1 1 : 2

2 2 : 5

3 5 : 2

4 5 : 4

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