$Assertion$: On a rainy day,it is difficult to drive a car or bus at high speed.
$Reason$: The value of the coefficient of friction is lowered due to the wetting of the surface.

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring some elongation and then released.

Two blocks of mass $2 \ kg$ and $1 \ kg$ are connected by an ideal spring on a rough surface. The spring is unstretched. The spring constant is $8 \ N/m$. The coefficient of friction is $\mu = 0.8$. Now,the $2 \ kg$ block is imparted a velocity $u$ towards the $1 \ kg$ block. Find the maximum value of velocity $u$ of the $2 \ kg$ block such that the $1 \ kg$ block never moves.

Which is a suitable method to decrease friction?

$A$ projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} \text{ m/s}$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground,$0.5 \text{ s}$ after the splitting. The other part,$t$ seconds after the splitting,falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g = 10 \text{ m/s}^2$.
$(1)$ The value of $t$ is. . . . . .
$(2)$ The value of $x$ is. . . . .

$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?