Question

A particle of mass m moving along a straight line experiences force F which varies with the distance x 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. $\sqrt{\frac{2F_0{x}_0}{m}}$
• C. $2\sqrt{\frac{F_0{x}_0}{m}}$
• D. none of these

Answer 1

Answer: (D)

none of these

Increase in KE = work done by all forces

$\Delta KE=F_{net}\cdot ds$
$\frac{1}{2}m{v}_2^2-\frac{1}{2}m\times \left(\frac{2F_0{x}_0}{m}\right)=\frac{1}{2}(2F_0+F_0)3x_0$
$\Rightarrow v_2=\sqrt{\frac{11F_0{x}_0}{m}}$