question_answer

A body executing SHM has its velocity 10 cm/s and 7 cm/s, when its displacements from the mean position are 3 cm and 4 cm, respectively The length of path is :

A)  10cm       

B)  9.5cm

C)  4cm        

D)  11.36cm

Correct Answer: B

Solution :

 Key Idea: Length of path is twice of amplitude. The velocity (u) of a body in SHM changes with displacement (y) as follows \[u=\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] where a is amplitude and co is angular speed.   Given, \[{{u}_{1}}=10\,cm/s,\,{{u}_{2}}=7\,cm/s\] \[{{y}_{1}}=3\,cm,\,{{y}_{2}}=4\,cm\] \[\therefore \] \[\frac{{{u}_{2}}}{{{u}_{1}}}=\frac{7}{10}=\sqrt{\frac{{{a}^{2}}-16}{{{a}^{2}}-9}}\] \[\Rightarrow \] \[a=4.77\,cm\] Length of path \[=2\,a=2\times 4.77\approx 9.5\]