Question

Two masses $10kg$ and $20kg$ are connected by a massless spring.A force of $200N$ acts on $20kg$ mass . At the instant when the $10kg$ mass has an acceleration $12m/s^2$ the energy stored in the spring $(k=2400N/m)$ will be

• A. $30J$
• B. $3J$
• C. $\sqrt{3}J$
• D. $80J$

Answer 1

The correct option is B $3J$

Two masses $10kg$ and $20kg$ are connected by a massless spring

A force $=200N$

On the mass $=20kg$

At the instant when the $10kg$

Mass has an acceleration $=12m/s^2$

Energy stored in the spring

$\left[m_1\right]>Kx$

$\left[m_2\right]>200N$
Sum of the horizontal forces on

$m_2=m_2\times a_2=F-Kx$

Sum of the horizontal forces on

$m_1=m_1\times a_1=Kxx=\frac{m_1{a}_1}{K}=\frac{10Kg\times 12m/s^2}{2400}=0.05m$

So, the spring is stretched out

$=0.05m$

Spring PE$=\frac{1}{2}K{x}^2=\frac{1}{2}\times 2400N/m\times (0.05{)}^2=1200\times \frac{25}{100}\times \frac{1}{100}=3J$