When a spring is stretched by $2\,\, cm$ , it stores $100\,\, J$ of energy. If it is stretched further by $2\,\, cm$ , the stored energy will be increased by ............. $\mathrm{J}$

Two similar springs $P$ and $Q$ have spring constants $K_P$ and $K_Q$, such that $K_P > K_Q .$ They are stretched first by the same amount (case $a$), then by the same force (case $b$). The work done by the springs $W_P$ and $W_Q$ are related as, in case $(a)$ and case $(b)$ respectively

Two masses $m_1 = 2\,kg$ and $m_2 = 5\,kg$ are moving on a frictionless surface with velocities $10\,m/s$ and $3\,m/s$ respectively. An ideal spring is attached on the back of $m_2$ . The maximum compression of the spring will be ............... $\mathrm{m}$

A block of mass $m$ is pushed against a spring whose spring constant is $k$ fixed at one end with a wall. The block can slide on a frictionless table as shown in figure. If the natural length of spring is $L_0$ and it is compressed to half its length when the block is released, find the velocity of the block, when the spring has natural length

Two identical blocks $A$ and $B$, each of mass $'m'$  resting on smooth floor are connected by a light spring of natural length $L$ and spring constant $K$, with the spring at its natural length. $A$ third identical block $'C'$ (mass $m$) moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$. the maximum compression in the spring is

A mass of $1\, kg$ is hanging from a spring of spring constant $1\, N/m$. If Saroj pulls the mass down by $2\,m$. The work done by Saroj is......$J$