$A$ truck starting from rest moves with an acceleration of $5\,m/s^2$ for $1\,sec$ and then moves with constant velocity. The velocity w.r.t. ground v/s time graph for the block in the truck is (Assume that the block does not fall off the truck and the coefficient of friction $\mu = 0.2$):

$A$ $20 \text{ ton}$ truck is travelling along a curved path of radius $240 \text{ m}$. If the center of gravity of the truck above the ground is $2 \text{ m}$ and the distance between its wheels is $1.5 \text{ m}$, the maximum speed of the truck with which it can travel without toppling over is (Acceleration due to gravity $= 10 \text{ ms}^{-2}$) (in $\text{ ms}^{-1}$)

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball:
$(1)$ remains stationary if there is no friction between the paper and the ball.
$(2)$ moves to the left and starts rolling backwards,i.e.,to the left,if there is friction between the paper and the ball.
$(3)$ moves forward,i.e.,in the direction in which the paper is pulled.
Here,the correct statement$(s)$ is/are:

$A$ bead of mass $m$ can slide on a frictionless fixed ring of radius $r$. With the help of two identical springs of force constant $k$,it is connected to two diametrically opposite nails $A$ and $B$,each of which is at a distance $0.5r$ from the centre $O$ of the ring. The relaxed length of each spring is negligible compared to the radius of the ring. The bead is given a small velocity. What can you predict for the further motion of the bead before any of the springs strikes a nail?

On which factors does the stopping distance of a vehicle depend?

$A$ $10 \, kg$ ball attached to the end of a rigid massless rod of length $L = 1 \, m$ rotates at a constant speed in a horizontal circle of radius $r = 0.5 \, m$ and period $T = 1.57 \, s$ as shown in the figure. The force exerted by the rod on the ball is ........ $N$.