Question

A 42.5 kg 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 1.84 s 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

Answer: (B)

40.5 kg

Answer 2

T = 2π $\sqrt { \frac { \mathrm { M } } { \mathrm { k } } }$

or $\left( \frac { T _ { 2 } } { T _ { 1 } } \right) ^ { 2 } = \frac { M + M _ { \text {Lady } } } { M }$

⇒ $\left( \frac { 1.84 } { 1.3 } \right) ^ { 2 }$= (1.40)² = 1.96 = 1 + $\frac { \mathrm { M } _ { \text {lady } } } { 42.5 }$

M_lady = 42.5 × 0.96 = 40.5 kg