A ball of mass $2 \,m$ and a system of two balls with equal masses $m$ connected by a massless spring, are placed on a smooth horizontal surface (see figure below). Initially, the ball of mass $2 \,m$ moves along the line passing through the centres of all the balls and the spring, whereas the system of two balls is at rest. Assuming that the collision between the individual balls is perfectly elastic, the ratio of vibrational energy stored in the system of two connected balls to the initial kinetic energy of the ball of mass $2 \,m$ is
$1$
$\frac{4}{9}$
$\frac{1}{2}$
$\frac{2}{3}$
The $P.E.$ of a certain spring when stretched from natural length through a distance $0.3\, m$ is $10\, J$. The amount of work in joule that must be done on this spring to stretch it through an additional distance $0.15\, m$ will be ................ $\mathrm{J}$
Whether the spring force is conservative or non-conservative ?
A spring of spring constant $ 5 \times 10^3$ $ N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\,cm$ is .............. $\mathrm{N-m}$
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