Question

A body is moving under the action of two forces ${\overline{F}}_1=2\hat{i}-5\hat{j};{\overline{F}}_2=3\hat{i}-4\hat{j}$. Its velocity will become uniform under a third force ${\overline{F}}_3$ given by

• A. $5\hat{i}-\hat{j}$
• B. $-5\hat{i}-\hat{j}$
• C. $5\hat{i}+\hat{j}$
• D. $-5\hat{i}+9\hat{j}$

Answer 1

The correct option is D $-5\hat{i}+9\hat{j}$

For uniform velocity, acceleration is zero. Hence resultant force will be zero.
$\therefore {\overline{F}}_1+{\overline{F}}_2+{\overline{F}}_3=0$
$(2\hat{i}-5\hat{j})+(3\hat{i}-4\hat{j})+{\overline{F}}_3=0$
or ${\overline{F}}_3=-5\hat{i}+9\hat{j}$