MHT CET · Physics · Laws of Motion

If a ship of mass \(4 \times 10^{7} \mathrm{~kg}\) initially at rest is pulled by a force of \(5 \times 10^{4} \mathrm{~N}\) through a distance of \(4 \mathrm{~m}\), then the speed of the ship will be (resistance due to water is negligible)

A \(5 \mathrm{~ms}^{-1}\)
B \(1.5 \mathrm{~ms}^{-1}\)
C \(60 \mathrm{~ms}^{-1}\)
D \(0.1 \mathrm{~ms}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(0.1 \mathrm{~ms}^{-1}\)

Step-by-step Solution

Detailed explanation

Using, \(F=m a\)
\(5 \times 10^{4} =4 \times 10^{7} \times a \)
\(\Rightarrow \quad a=\frac{5 \times 10^{4}}{4 \times 10^{7}}=\frac{5}{4} \times 10^{-3} \mathrm{~ms}^{-2}\)
Given, \(s=4 \mathrm{~m}, 4=0 \quad \therefore v^{2}=u^{2}+2\) as
or
\(=0+2 \times \frac{5}{4} \times 4 \times 10^{-3}\)
\(v^{2}=10^{-2}\)
or
\(v=0.1 \mathrm{~ms}^{-1}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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