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 ............. $\mathrm{cm}$

A block is attached to a spring as shown and very-very gradually lowered so that finally  spring expands by $"d"$. If same block is attached to spring & released suddenly then maximum expansion in spring will be-

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

Show that the law of conservation of mechanical energy is obeyed by pulling or compressing the block tied at the end of a spring.

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block 

To an observer $B$, when the block is compressing the spring

This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.

Statement $-1$: If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$

Statement $-2$ : $k_1 < k_2$.