$A$ vessel containing water is moving with a constant speed towards the right along a straight horizontal path. If the vessel is given a constant retardation towards the right along a straight line,which of the following diagrams represents the surface of the liquid?

$A$ very broad elevator is going up vertically with a constant acceleration of $2\,m/s^2$. At the instant when its velocity is $4\,m/s$,a ball is projected from the floor of the lift with a speed of $4\,m/s$ relative to the floor at an elevation of $30^{\circ}$. The time taken by the ball to return to the floor is $..............\,s$ $(g=10\,m/s^2)$.

An object dropped in a stationary lift takes time $t_1$ to reach the floor. It takes time $t_2$ when the lift is moving up with constant acceleration. Then

$A$ piece of wire is bent in the shape of a parabola $y=kx^2$ ($y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead,where the bead can stay at rest with respect to the wire,from the $y$-axis is

$A$ block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

If a body of mass $m$ is carried by a lift moving with an upward acceleration $a$,then the forces acting on the body are:
$(i)$ The reaction $R$ on the floor of the lift acting upwards.
$(ii)$ The weight $mg$ of the body acting vertically downwards.
The equation of motion will be given by: