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

$A$ block '$A$' takes $2\,s$ to slide down a frictionless incline of $30^{\circ}$ and length '$l$',kept inside a lift going up with uniform velocity '$v$'. If the incline is changed to $45^{\circ}$,the time taken by the block to slide down the incline will be approximately $........\,s$.

$A$ body is slipping from an inclined plane of height $h$ and length $l$. If the angle of inclination is $\theta$,the time taken by the body to come from the top to the bottom of this inclined plane is

$A$ football of radius $R$ is kept on a hole of radius $r$ (where the diameter of the hole is $2r$ and $r < R$) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted,making an angle $\theta$ with the horizontal as shown in the figure. The maximum value of $\theta$ such that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) -

Describe Galileo's experiment of an inclined plane regarding motion.

$A$ car is moving on a plane inclined at $30^{\circ}$ to the horizontal with an acceleration of $10 \, ms^{-2}$ parallel to the plane upward. $A$ bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ...... . (Take $g = 10 \, ms^{-2}$)