Question

A particle of mass $m$ moving along a straight-line experiences force 𝐹 which varies with the distance travelled as shown in the figure. If the velocity of the particle at $x_0$ is $\sqrt{\frac{2F_0{x}_0}{m}}$, then velocity at $4x_0$ is:

• A. $2\sqrt{\frac{2F_0{x}_0}{m}}$
• B. $2\sqrt{\frac{F_0{x}_0}{m}}$
• C. $\sqrt{\frac{F_0{x}_0}{m}}$
• D. none of these

Answer 1

The correct option is D none of these

Initial velocity at $x_0=\sqrt{\frac{2F_0{x}_0}{m}}$

Initial distance $=x_0$

Final distance$=4x_0$

Increase in $KE=$ Work done
$\frac{1}{2}m{v}_2^2-\frac{1}{2}m\times \left(\frac{2F_0{x}_0}{m}\right)=\frac{1}{2}\times [2F_0+F_0]\cdot 3x_0$

$\Rightarrow v_2=\sqrt{\frac{11F_0{x}_0}{m}}$

Final Answer: (d)