Question

A body of mass $2\text{kg}$ has an initial velocity of $3m/s$ along $OE$ and it is subjected to a force of $4\text{N}$ in a direction perpendicular to $OE$. The magnitude of displacement of the body from $O$ after 4 seconds will be

• A. $12\text{m}$
• B. $20\text{m}$
• C. $32\text{m}$
• D. $48\text{m}$

Answer 1

The correct option is B $20\text{m}$


Displacement of body in $4\text{s}$ along $OE$
$s_x=u_{x}t=3\times 4=12\text{m}$
Force along $OF$ (perpendicular to $OE$)
$=4\text{N}$
$\therefore a_y=\frac{F}{m}=\frac{4}{2}=2{\text{m/s}}^2$
Displacement of body in $4\text{s}$ along $OF$
$\Rightarrow s_y=u_{y}t+\frac{1}{2}{a}_y{t}^2=0+\frac{1}{2}\times 2\times (4{)}^2=16\text{m}[\text{As}{u}_y=0]$
$\therefore$ Net displacemnet $s=\sqrt{s_x^2+s_y^2}=\sqrt{(12{)}^2+(16{)}^2}=20\text{m}$