Question

Two plates each of mass $m$ are connected by a massless spring as shown. A weight $W$ is put on the upper plate which compresses the spring further. When $W$ is removed, the entire assembly jumps up. The minimum weight $W$ needed for the assembly to jump up when the weight is removed is just more than:

• A. $mg$
• B. $2mg$
• C. $3mg$
• D. $4mg$

Answer 1

The correct option is B $2mg$

When $W$ is removed, the upper plate bounces up regardless of the weight $W$. The upper plate first reaches relaxation length and then further moves up extending the spring. On extension of spring, lower block feels an upward force.

For lower block to just lift, the upward force of the spring should be just greater than the mass of the lower plate.

$kx\ge mg$

Using conservation of energy at most compressed and most expanded positions, we get:

$\frac{k{h}^2}{2}=\frac{k{x}^2}{2}+mg(h+x)$

$k{h}^2-2mgh-(k{x}^2+2mgx)=0$

Substituting the value of $x$ and solving for $h$, we get

$h=\frac{3mg}{k}$

At position of largest compression,

$mg+W=kh$

$mg+W=3mg$

$W=2mg$