Three weights $W, 2W$,and $3W$ are connected to identical springs suspended from a rigid horizontal rod. The assembly of the rod and the weights falls freely under gravity. The positions of the weights from the rod are such that:

$A$ man is standing on a weighing machine placed in a lift. When stationary,his weight is recorded as $40 \, kg$. If the lift is accelerated upwards with an acceleration of $2 \, m/s^2$,then the weight recorded in the machine will be .......... $kg$ $(g = 10 \, m/s^2)$.

$A$ solid sphere of mass $2\, kg$ is resting inside a cube as shown in the figure. The cube is moving with a velocity $\vec v = (5t\,\hat i + 2t\,\hat j)\,m/s$. Here $t$ is the time in seconds. All surfaces are smooth. The sphere is at rest with respect to the cube. Find the total force $N$ exerted by the sphere on the cube. (Take $g = 10\, m/s^2$)

$A$ weight is suspended from the ceiling of a lift by a spring balance. When the lift is stationary,the spring balance reads $W$. If the lift suddenly falls freely under gravity,the reading on the spring balance will be

Why do we feel dizzy when riding a giant wheel (Ferris wheel) rotating in a vertical plane?

The horizontal acceleration that should be given to a smooth inclined plane of angle $\theta = \sin^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane,relative to the inclined plane is: