question_answer

A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is :- (take\[\text{g}=\text{1}0\text{m}{{\text{s}}^{\text{2}}}\]) [JEE Main Solved Paper-2016 ]

A) \[\sqrt{2}s\]                                      

B) \[2\pi \sqrt{2}s\]

C) \[2s\]                                   

D) \[2\sqrt{2}s\]

Correct Answer: D

Solution :

                Velocity at point\[P=\sqrt{\frac{\frac{m}{L}gx}{m/L}}\]\[v=\sqrt{gx}\] \[\frac{dx}{dt}=\sqrt{gx}\]                          \[\int\limits_{0}^{20}{\frac{dx}{\sqrt{x}}=\int\limits_{0}^{t}{\sqrt{g}}dt}\] \[\]