A block of mass $\sqrt{2}\,kg$ is released from the top of an inclined smooth surface as shown in figure. If spring constant of spring is $100\,N / m$ and block comes to rest after compressing the spring by $1 \,m$, then the distance travelled by block before it comes to rest is ......... $m$

A block is fastened to a horizontal spring. The block is pulled to a distance $x =10\,cm$ from its equilibrium position (at $x =0$ ) on a frictionless surface from rest. The energy of the block at $x =5$ $cm$ is $0.25\,J$. The spring constant of the spring is $.........Nm ^{-1}$

A $0.5 \,kg$ block moving at a speed of $12 \,ms ^{-1}$ compresses a spring through a distance $30\, cm$ when its speed is halved. The spring constant of the spring will be $Nm ^{-1}$.

The length of a spring is a when $\alpha $ force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is

A spring when stretched by $2 \,mm$ its potential energy becomes $4 \,J$. If it is stretched by $10 \,mm$, its potential energy is equal to

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