$A$ particle of mass $m$ falls from rest through a resistive medium having a resistive force, $F = -kv$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$?

Match the items in Column-$I$ with those in Column-$II$.

Column-$I$	Column-$II$
$(1)$ Definition of force	$(a)$ Newton's third law of motion
$(2)$ Measurement of force	$(b)$ Newton's second law of motion
	$(c)$ Newton's first law of motion

Masses of $10\, kg$ and $20\, kg$ are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant shown,the $10\, kg$ mass has an acceleration of $12\, m/s^2$. What is the acceleration of the $20\, kg$ mass in $m/s^2$?

$A$ gardener holds a hosepipe through which water is gushing out at a rate of $4\, kg\, s^{-1}$ with a speed of $2\, ms^{-1}$. The moment the speed of water is increased to $3\, ms^{-1}$,the gardener will experience a jerk of

$A$ mass of $1 \text{ kg}$ is kept on an inclined plane with $30^\circ$ inclination with respect to the horizontal plane and it is at rest initially. Then, the whole assembly is moved up with a constant velocity of $4 \text{ m/s}$. The work done by the frictional force in time $2 \text{ s}$ is . . . . . . $\text{J}$. (Take $g = 10 \text{ m/s}^2$)

The figure shows an arrangement of a rod of length $l$ and mass $M$ and a bead of mass $m$ attached to a weightless string passing over a frictionless pulley. At $t = 0$,the bead is level with the lower end of the rod. The bead slides down the string with considerable friction and is opposite to the other end of the rod after $T$ seconds. Assuming friction between the bead and the string to be constant throughout,the frictional force is: