The friction coefficient between the horizontal surface and each of the blocks shown in the figure is $\mu = 0.2$. The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest? (in $cm$)

$A$ bullet of $10\, \text{g}$, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100\, \text{m/s}$. The length of the pendulum is $0.5\, \text{m}$ and the mass of the bob is $1\, \text{kg}$. The minimum value of $v$ in $\text{m/s}$ so that the pendulum completes a vertical circle is: (Assume the string to be inextensible and $g=10\, \text{m/s}^2$)

$A$ body of mass $2 \,kg$ is moving with a constant acceleration of $(2 \hat{i}+3 \hat{j}-\hat{k}) \,ms^{-2}$. If the displacement made by the body is $(3 \hat{i}-\hat{j}+2 \hat{k}) \,m$, then the work done is: (in $\,J$)

Identify the correct statements from the following:
$(A)$ Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
$(B)$ Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
$(C)$ Work done by friction on a body sliding down an inclined plane is positive.
$(D)$ Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.
$(E)$ Work done by the air resistance on an oscillating pendulum is negative.
Choose the correct answer from the options given below:

Two blocks $A(5 \ kg)$ and $B(2 \ kg)$ attached to the ends of a spring of spring constant $k = 1120 \ N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously,velocities of $3 \ m/s$ and $10 \ m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$. Then:

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