An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is
$\frac{1}{2} Ky ^2$
$\frac{1}{2}Ky(2x+y)$
$\frac{1}{2}K(x^2+y^2)$
$\frac{1}{2} k(x+y)^2$
$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$, the work done by spring force is
A ball of mass $m_1$ falls from height $h_1$ from rest to strike a spring of force constant $K$, which forces another ball of mass $m_2$ to jump on a horizontal floor at a height $h_2$ below from it. Find the horizontal distance at which ball of mass $m_2$ strikes from the position of start :- [Spring does not move]
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
A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$. Initially the spring is in its natural length. Velocity of the container at the instant compression in spring is maximum for the first time :-
$A$ 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: