Question

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

• A. 12 m
• B. 20 m
• C. 8 m
• D. 48 m

Answer 1

Answer: (B)

The acceleration of the body perpendicular to $ OE $ is
$ a=\frac{F}{m}=\frac{4}{2}=2\,m/{{s}^{2}} $
Displacement along OE,
$ {{s}_{1}}=vt=3\times 4=12\,m $
Displacement perpendicular to OE
$ {{s}_{2}}=\frac{1}{2}a{{t}^{2}} $
$ =\frac{1}{2}\times 2\times {{(4)}^{2}}=16\,m $
The resultant displacement
$ s=\sqrt{s_{1}^{2}+s_{2}^{2}} $
$ =\sqrt{144+256} $
$ =\sqrt{400} $
$ =20\,m $