Question 7: Motion in 2D & Vectors

Question

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

Accepted Answer

Mass of the body is
$$ m=100	ext{ g}=0.1	ext{ kg} $$
The force acting on it is
$$ \vec F = 5\hat i + 10\hat j $$
Using NewtonÃ¢ÂÂs second law,
$$ \vec a=\frac{\vec F}{m} $$
So,
$$ \vec a=\frac{5\hat i+10\hat j}{0.1} =50\hat i+100\hat j $$
Hence,
acceleration in $x$-direction: $a_x=50	ext{ m/s}^2$
acceleration in $y$-direction: $a_y=100	ext{ m/s}^2$
Since the body starts moving at $t=0$, we take initial velocity as zero.
Using
$$ s=ut+\frac{1}{2}at^2 $$
for $t=2	ext{ s}$:
In $x$-direction,
$$ s_x=0+\frac{1}{2}(50)(2)^2 =25	imes 4=100	ext{ m} $$
In $y$-direction,
$$ s_y=0+\frac{1}{2}(100)(2)^2 =50	imes 4=200	ext{ m} $$
Given position after $2$ s is
$$ (2x\hat i+5y\hat j)	ext{ m} $$
So,
$$ 2x=100 \quad\Rightarrow\quad x=50 $$
and
$$ 5y=200 \quad\Rightarrow\quad y=40 $$
Therefore,
$$ x:y=50:40=5:4 $$
So the correct answer is:
$$ \boxed{5:4} $$
Option D

Answer

$1: 2$

Answer

$2: 5$

Answer

$5 : 2$

Answer

$5: 4$

Motion in 2D & Vectors

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} \cdot After 2 s its position is (2 x \hat{\mathrm{i}}+5 y \hat{\mathrm{j}}) \mathrm{m}. The ratio x: y is \_\_\_\_ .

Choose the correct answer: