Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, s$,the combined mass travels ............ $m$.

$A$ ball is allowed to fall from a height of $10 \, m$. If there is $40 \%$ loss of energy due to impact,then after one impact the ball will rise to a height of ........ $m$.

$A$ chain of length $L = 2 \ m$ is placed on a smooth table such that half of its length hangs over the edge. If the chain is released,find the velocity of the chain when it just leaves the table (in $m/s$). (Take $g = 10 \ m/s^2$)

$A$ mass of $2.9 \ kg$ is suspended from a string of length $50 \ cm$ and is at rest. Another body of mass $100 \ g$,which is moving horizontally with a velocity of $150 \ m/s$,strikes and sticks to it. Subsequently,when the string makes an angle of $60^{\circ}$ with the vertical,the tension in the string is $(g = 10 \ m/s^2)$. (in $N$)

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
$(a)$ Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
$(b)$ Work done by gravitational force in the above case.
$(c)$ Work done by friction on a body sliding down an inclined plane.
$(d)$ Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
$(e)$ Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

Two bodies $A$ and $B$ of masses $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring. $A$ third body $C$ of mass $m$ moves with velocity $V_0$ along the line joining $A$ and $B$ and collides elastically with $A$ as shown in the figure. At a certain instant of time $t_0$ after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same. Further,at this instant,the compression of the spring is found to be $x_0$. Determine the spring constant $k$.