Three masses 500 g , 300 g and 100 g are suspended at the end of spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 2 second. When

Question

Three masses 500 g , 300 g and 100 g are suspended at the end of spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 2 second. When the 300 g mass is also removed it will oscillate with a period of

TestHub · Accepted Answer

The time period of oscillation for a spring-mass system is given by $T = 2 π \frac{m}{k}$ , where $m$ is the oscillating mass and $k$ is the spring constant.

When the $500 g$ mass is removed, the remaining mass attached to the spring is $m_{1} = 100 g + 300 g = 400 g$ .

The time period in this case is $T_{1} = 2 π \frac{400}{k} = 2 s$ .

When the $300 g$ mass is also removed, the remaining mass is $m_{2} = 100 g$ .

The new time period is $T_{2} = 2 π \frac{100}{k}$ .

Taking the ratio of the two time periods, we get:

$\frac{T _{2}}{T _{1}} = \frac{m _{2}}{m _{1}} = \frac{100}{400} = \frac{1}{4} = \frac{1}{2}$

Substituting $T_{1} = 2 s$ :

$T_{2} = 2 \times \frac{1}{2} = 1 s$

Answer: 1 s

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion