One end of a spring of force constant 150 dyne \(\mathrm{cm}^{-1}\) is connected to a block of mass \(0.2 \mathrm{~kg}\) kept on a rough horizontal surface of coefficient of friction 0.3 . The other end of the spring is connected to a rigid support as shown in the figure and the spring is initially undeformed. The maximum velocity \(\mathrm{v}\) that can be given to the block so that it travels only in one direction is ____ \(\mathrm{ms}^{-1}\). (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\))

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.