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

$A$ trolley is sliding freely down an inclined plane as shown in the figure. The angle $(\alpha)$ that the string of the pendulum makes with the ceiling of the trolley is equal to ..........

$A$ body of mass $2 \, kg$ is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity $g$,the reading on the spring balance will be ....... $kg$.

Given below are two statements:
Statement-$I$: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement-$II$: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.
In the light of the above statements,choose the correct answer from the options given below:

$A$ body of mass $2 \, kg$ is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity $g$,and if the lift moves up with a constant velocity of $2 \, m/s$,the reading on the balance will be ......... $kg$.

$A$ man is standing in a lift which goes up and comes down with the same constant acceleration. If the ratio of the apparent weights in the two cases is $2 : 1$,then the acceleration of the lift is ......... $m/s^2$.