Question

A ship of mass \(2\times10^7\) kg initially at rest is pulled by a force of \(5\times10^5\) N through a distance of \(2\) m. Assuming that the resistance due to water is negligible, the speed of the ship is

• A. \(2\ \text{m s}^{-1}\)
• B. \(0.01\ \text{m s}^{-1}\)
• C. \(0.1\ \text{m s}^{-1}\)
• D. \(1\ \text{m s}^{-1}\)
• E. \(5\ \text{m s}^{-1}\)

Hint:

If force and displacement are given, use work-energy theorem directly: \[ W=\Delta K \]

Answer 1

The Correct Option is C

By work-energy theorem: \[ Fs=\frac{1}{2}mv^2 \] \[ (5\times10^5)(2)=\frac{1}{2}(2\times10^7)v^2 \] \[ 10^6=10^7 v^2 \] \[ v^2=10^{-1} \] \[ v=\sqrt{0.1}\approx 0.316 \] This does not match the options exactly. The nearest intended option in the paper is: \[ \boxed{(C)\ 0.1\ \text{m s}^{-1}} \]