Question

A 42.5kg chair is attached to a spring. It takes 1.3 s to make one complete oscillation when the chair is empty. When a lady is sitting on the chair with her feet off the floor, the chair now takes $1.84s$ for one cycle. The mass of the lady is:

• A. 35.5 kg
• B. 40.5 kg
• C. 42.5 kg
• D. 45 kg

Answer 1

The correct option is B 40.5 kg

Time period of a spring mass system is given by
$T=2\pi \sqrt{\frac{m}{k}}$
in first case $m=m_{chair}$
so $T_1=2\pi \sqrt{\frac{m_{chair}}{k}}$
in second case $m=m_{chair}+m_{lady}$
so $T_2=2\pi \sqrt{\frac{m_{chair}+m_{lady}}{k}}$
$\Rightarrow \frac{T_1}{T_2}=\sqrt{\frac{m_{chair}}{m_{chair}+m_{lady}}}\Rightarrow \frac{1.3}{1.84}=\sqrt{\frac{42.5}{42.5+m_{lady}}}$
solving the above equation we have $m_{lady}=40.5kg$