$A$ mass of $1 \; kg$ collides elastically with a stationary mass of $5 \; kg$. After the collision,the $1 \; kg$ mass moves in the opposite direction with a velocity of $2 \; ms^{-1}$. Which of the following statements is correct for this system of two masses?

$A$ block of mass $5 \ kg$ is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration $2 \ m/s^2$. The work done by tension on the block during the first $3 \ s$ is $(u = 0)$. (in $J$)

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.

$A$ ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $x$-axis,hits another ball of mass $20\, kg$ which is at rest. After the collision,the first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along the $y$-axis with a speed of $10 \, m/s$. The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x$-axis. The velocity of the ball moving at $30^{\circ}$ with the $x$-axis is $x \, m/s$. The configuration of pieces after the collision is shown in the figure. The value of $x$ to the nearest integer is:

$A$ tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.

$A$ small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has a coefficient of friction $\mu$. The ball comes to a stop at $C$ after traveling a distance $L$. The value of $L$ is: