Question

A body of mass \(2\) kg is moving with a momentum of \(10\ \text{kg m s}^{-1}\). The force needed to increase its kinetic energy four times in \(10\) seconds is

• A. \(2\) N
• B. \(4\) N
• C. \(1\) N
• D. \(0.5\) N
• E. \(8\) N

Hint:

If kinetic energy becomes four times, speed becomes twice, because \(K\propto v^2\).

Answer 1

The Correct Option is D

Initial momentum: \[ p=10 \] Mass: \[ m=2 \] Initial speed: \[ v=\frac{p}{m}=\frac{10}{2}=5\ \text{m s}^{-1} \] Initial kinetic energy: \[ K=\frac12 mv^2=\frac12(2)(25)=25\text{ J} \] Four times kinetic energy: \[ K'=100\text{ J} \] So final speed: \[ \frac12 (2)v'^2=100 \Rightarrow v'^2=100 \Rightarrow v'=10\ \text{m s}^{-1} \] Acceleration: \[ a=\frac{v'-v}{t}=\frac{10-5}{10}=0.5\ \text{m s}^{-2} \] Force: \[ F=ma=2\times0.5=1\text{ N} \] So the direct calculation gives: \[ \boxed{1\text{ N}} \] which corresponds to option (C), not (D).