Question

A $7kg$ object is subjected two forces (in Newton) ${\overrightarrow{F}}_1=20\hat{i}+30\hat{j}$ and ${\overrightarrow{F}}_2=8\hat{i}-5\hat{j}$. The magnitude of resulting acceleration in $m{s}^{-2}$ will be.

• A. $5$
• B. $4$
• C. $3$
• D. $2$

Answer 1

The correct option is A $5$

Given,

$m=7kg$

${\overrightarrow{F}}_1=20\hat{i}+30\hat{k}$

${\overrightarrow{F}}_2=8\hat{i}-5\hat{j}$

The net force is equal to the sum of two force,

$\overrightarrow{F}={\overrightarrow{F}}_1+{\overrightarrow{F}}_2$

$\overrightarrow{F}=20\hat{i}+30\hat{j}+8\hat{i}-5\hat{j}=28\hat{i}+25\hat{j}$

Magnitude, $|\overrightarrow{F}|=\sqrt{(28{)}^2+(25{)}^2}=35N$

Force, $F=ma$

$a=\frac{F}{m}$

acceleration, $a=\frac{37.5}{7}=5m/s^2$.

The acceleration is $5m/s^2$.

The correct option is A.