Question

The period of a spring-mass system ios directly proportional to the square root of the mass. Originally, the period of the system was 2.0 seconds. The original mass was 1.0 kg.
Which value shown is closest to the new period if the new mass is 24.0 kg?

• A. 48 seconds
• B. 24 seconds
• C. 10 seconds
• D. 22 seconds
• E. 8 seconds

Answer 1

The correct option is C 10 seconds

Given : $M_1=1.0$ kg $T_1=2.0$ seconds $M_2=24.0$ kg

Time period of spring-mass system $T\propto \sqrt{M}$ $⟹\frac{T_2}{T_1}=\sqrt{\frac{M_2}{M_1}}$

$\therefore$ $\frac{T_2}{2.0}=\sqrt{\frac{24.0}{1.0}}$ $⟹T_2=9.8$ $\approx 10$ seconds