An elevator car,whose floor-to-ceiling distance is $2.7 \, m$,starts ascending with a constant acceleration of $1.2 \, m/s^2$. $2 \, s$ after the start,a bolt begins falling from the ceiling of the car. The free-fall time of the bolt is ......... $s$.

$A$ wooden block of mass $5 \, kg$ rests on a soft horizontal floor. When an iron cylinder of mass $25 \, kg$ is placed on top of the block, the floor yields and the block and the cylinder together move down with an acceleration of $0.1 \, m/s^2$. The action force of the system on the floor is equal to: (in $N$)

$A$ car is moving with a constant speed of $20\,m/s$ on a circular horizontal track of radius $40\,m$. $A$ bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take $g = 10\,m/s^2$)

$A$ lift is accelerating downward with an acceleration $a$. $A$ man inside the lift throws a ball upward with an acceleration $a_0$ relative to the lift $(a_0 < a)$. What is the acceleration of the ball as observed by an observer on the Earth?

The minimum acceleration that must be imparted to the cart in the figure so that the block $A$ will not fall (given $\mu$ is the coefficient of friction between the surfaces of the block and the cart) is given by

$A$ circular table is rotating with an angular velocity of $\omega \text{ rad/s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. $A$ steel ball is gently placed at a distance of $1 \text{ m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \text{ m}$,the radial velocity of the ball with respect to the table at the time the ball leaves the table is $x \sqrt{2} \omega \text{ m/s}$,where the value of $x$ is............