Two bodies $A$ and $B$ of mass $m$ and $2\, m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_0$. The spring constant $k$ will be
$m\,\frac{{v_0^2}}{{x_0^2}}$
$m\,\frac{{{v_0}}}{{2{x_0}}}$
$2m\,\frac{{{v_0}}}{{{x_0}}}$
$\frac{2}{3}m\,{\left( {\frac{{{v_0}}}{{{x_0}}}} \right)^2}$
Two identical blocks $A$ and $B$ each of mass $m$ resting on the smooth horizontal floor are connected by a light spring of natural length $L$ and spring constant $K$. A third block $C$ of 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 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 ......... $m$
Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.
A spring of force constant $10\, N/m$ has an initial stretch $0.20\, m.$ In changing the stretch to $0.25\, m$, the increase in potential energy is about.....$joule$
A one kg block moves towards a light spring with a velocity of $8\, m/s$. When the spring is compressed by $3\, m$, its momentum becomes half of the original momentum. Spring constant of the spring is :-