Question

The figure above shows the same ideal spring in three different situations.
First, without a mass hanging, the spring is unstretched.
Next, with the blue mass hanging, the spring stretches.
Finally, with the red mass hanging, the spring stretches twice as much as it did with the blue mass.
How much does the red mass weigh, compared to the blue mass?

• A. The red mass weighs twice as much as the blue mass
• B. The red mass weighs four times as much as the blue mass
• C. The red mass weighs half as much as the blue mass
• D. The red mass weighs about $1.4$ times as much as the blue mass
• E. We cannot determine how much the red mass weighs compared to the blue mass, because we do not know the unstretched length of the spring

Answer 1

The correct option is A The red mass weighs twice as much as the blue mass

In equilibrium position of spring ,

weight of mass =restoring force of spring

as both the systems are in equilibrium therefore ,

for blue mass system ,

$m_{B}g=k{x}_B$

or $m_B=k{x}_B/g$ ................................eq1

for red mass system ,

$m_{R}g=k{x}_R$

or $m_R=k{x}_R/g$ ,

but given $x_R=2x_B$ ,

so $m_R=k\times 2x_B/g$ ..................................eq2

dividing eq2 by eq1 ,

$m_R/m_B=2$

or $m_R=2m_B$