A body of mass $1\,kg$ falls freely from a height of $100\,m,$ on a platform of mass $3\,kg$ which is mounted on a spring having spring constant $k = 1.25 \times 10^6\, N/m.$ The body sticks to the platform and the spring’s maximum compression is found to be $x.$ Given that $g = 10\,ms^{-2},$ the value of $x$ will be close to ……………. $\mathrm{cm}$

A spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel the force constant of the combination will be

A $2\ kg$ block slides on a horizontal floor with a speed of $4\ m/s$. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is $15\ N$ and spring constant is $10,000\ N/m$. The spring compresses by …………. $\mathrm{cm}$

Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.

Two blocks of mass $2\ kg$ and $1\ kg$ are connected by an ideal spring on a rough surface. The spring in unstreched. Spring constant is $8\ N/m$ . Coefficient of friction is  $μ = 0.8$ . Now block $2\ kg$ is imparted a velocity $u$ towards $1\ kg$ block. Find the maximum value of velocity $'u'$ of block $2\ kg$ such that block of $1\ kg$ mass never move is