A ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$ . Other end of spring is fixed and ring can slide on a smooth horizontal rod as shown. Now the ring is shifted to position $B$ and released, speed of ring when spring attains it's natural length is
$\frac{{2{l_0}}}{3}\sqrt {\frac{k}{m}} $
$\frac{{{l_0}}}{3}\sqrt {\frac{k}{m}} $
$\frac{{3{l_0}}}{2}\sqrt {\frac{k}{m}} $
${l_0}\sqrt {\frac{k}{m}} $
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 ............. $\mathrm{J}$
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 ............. $\mathrm{cm}$
The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$, potential energy stored in it will be $.......\,U$
A chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$ ). Calculate the work done to fold it as shown in diagram $(II)$
$A$ spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring an elongation less than $\frac{{2\mu mg}}{K}$ but more than $\frac{{\mu mg}}{K}$ and released. Which of the following laws/principles of physics can be applied on the spring block system