$A$ $1000\, kg$ elevator rises from rest in the basement to the fourth floor,a distance of $20\, m$. As it passes the fourth floor,its speed is $4\, m/s$. There is a constant frictional force of $500\, N$. The work done by the lifting mechanism is

Consider the following two statements: $[A]$ The linear momentum of a system is zero. $[B]$ The kinetic energy of the particles of the system is zero.

Starting from rest on her swing at initial height $h_0$ above the ground,Saina swings forward. At the lowest point of her motion,she grabs her bag that lies on the ground. Saina continues swinging forward to reach maximum height $h_1$. She then swings backward and when reaching the lowest point of motion again,she simply lets go of the bag,which falls freely. Saina's backward swing then reaches maximum height $h_2$. Neglecting air resistance,how are the three heights related?

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially, $S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision, $S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision:

Two bodies $A$ and $B$ of masses $2m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and $2u$ respectively. The ratio of the kinetic energy of body $A$ and the potential energy of body $B$ at a height equal to half of the maximum height reached by body $A$ is (in $ : 1$)

$A$ hammer of mass $M$ strikes a nail of mass $m$ with a velocity $20 \ m/s$ into a fixed wall. The nail penetrates into the wall to a depth of $1 \ cm$. The average resistance of the wall to the penetration of the nail is