$A$ small block of mass $m$ is placed on $a$ wedge of mass $M$ as shown, which is initially at rest. All the surfaces are frictionless . The spring attached to the other end of wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down, then Maximum velocity of $M$ is:
$\sqrt {2gh} $
$\sqrt {\frac{{2ghm}}{{m + M}}} $
$\sqrt {\frac{{2{m^2}gh}}{{mM + {M^2}}}} $
None
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 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
A $1\; kg$ block situated on a rough incline is connected to a spring of spring constant $100\;N m ^{-1}$ as shown in Figure. The block is released from rest with the spring in the unstretched position. The block moves $10 \;cm$ down the incline before coming to rest. Find the coefficient of friction between the block and the incline. Assume that the spring has a negligible mass and the pulley is frictionless.
Two springs have their force constant as ${k_1}$ and ${k_2}({k_1} > {k_2})$. When they are stretched by the same force
A block $(B)$ is attached to two unstretched springs $\mathrm{S} 1$ and $\mathrm{S} 2$ with spring constants $\mathrm{k}$ and $4 \mathrm{k}$, respectively (see figure $\mathrm{I}$ ). The other ends are attached to identical supports $M1$ and $M2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $\mathrm{B}$ is displaced towards wall $1$ by a small distance $\mathrm{x}$ (figure $II$) and released. The block returns and moves a maximum distance $\mathrm{y}$ towards wall $2$ . Displacements $\mathrm{x}$ and $\mathrm{y}$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is Figure: $Image$