Question

An object starts from rest and is acted upon by a variable force $F$ as shown in figure. If $F_{0}$ is the initial value of the force, then the position of the object, where it again comes to rest will be

• A. $\frac{2 F_{0}}{\tan \alpha}$
• B. $\frac{F_{0}}{\sin \alpha}$
• C. $\frac{2 F_{0}}{\cot \alpha}$
• D. $\frac{F_{8}}{2 \cos \alpha}$

Answer 1

Answer: (A)

$F-x$ curve is straight line. Equation of $F$ in terms of $x$ can be written as
$F=x \tan \alpha-F_{0}$
$a=\frac{v d v}{d x}=\frac{F}{m}=\frac{x \text { tan } \alpha}{m}-\frac{F_{0}}{m}$
Integrating both sides
$\frac{v^{2}-x^{2}}{2}=\frac{x^{2} \tan \alpha}{2 m}-\frac{F_{0} x}{m}=0$
$\frac{x \tan \alpha}{2}=F_{0}$
$x=\frac{2 F_{0}}{\tan \alpha}$