Question

On a table, a disc of mass $1kg$ is placed over which is placed a massless spring of length, $20cm$ and spring constant $105$ dynes/cm. Another disc of mass $2kg$ is placed on the spring and the system is allowed to come to rest. Now the table is suddenly removed. What is the instantaneous acceleration of the centre of mass?

• A. $\frac{g}{2}$
• B. $\frac{g}{3}$
• C. $g$
• D. $\frac{2g}{3}$

Answer 1

The correct option is B $\frac{g}{3}$

According to the given question,from the table if force is suddenly removed than (1+2=3N) of force was acting in it.
$3g=3f$
$g=f$
$(m_1+m_2)y=m_1{y}_1+m_2{y}_2$
$\frac{{\partial }^{2}y}{\partial t^2}=m_1{y}_1+m_2{y}_2$
$\frac{{\partial }^{2}y}{\partial t^2}=a$
This above concept is based on table point of view which is basically deals with respect to y-axis
$3\frac{{\partial }^{2}y}{\partial t^2}=1\times g+2\times 0$
$\frac{{\partial }^{2}y}{\partial t^2}=\frac{g}{3}$