question_answer

A mass m attached to a spring oscillates with time period 2 s. If the mass is increased by 2 kg, then time period increases by 1 s. Then the initial mass of the body will be :

A)  12.8kg        

B)  8.6kg

C)  1.6kg         

D)  3.2kg

Correct Answer: C

Solution :

The time period of spring mass system is given by \[T=2\,\pi \sqrt{\frac{m}{k}}\] where m is mass, and k is spring constant.                       Given, \[{{m}_{1}}=m,\,\,{{T}_{1}}=2\,s,\,{{T}_{2}}=2+1=3\,s\], \[\therefore \] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{m}{m+2}}\] \[\therefore \] \[\frac{2}{3}=\sqrt{\frac{m}{m+2}}\] \[\Rightarrow \] \[\frac{9}{4}=\frac{m+2}{m}\] \[\Rightarrow \] \[9m=4m+8\] \[\Rightarrow \] \[m=1.6\,kg\].