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

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant the compression in the spring is maximum for the first time.

$A$ 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 .......... $kg$ $(g = 10 \, m/s^2)$.

$A$ metallic rod of length $L$ and mass $M$ is moving under the action of two unequal forces $F_1$ and $F_2$ (directed opposite to each other) acting at its ends along its length. Ignore gravity and any external magnetic field. If the specific charge of electrons is $(e/m)$,then the potential difference between the ends of the rod in steady state must be:

The mass of a person sitting in a lift is $50 \, kg$. If the lift is coming down with a constant acceleration of $10 \, m/s^2$,then the reading of the spring balance will be ......... $N$ $(g = 10 \, m/s^2)$.

$A$ car moving with a speed of $54 \text{ km/h}$ takes a turn of radius $20 \text{ m}$. $A$ simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10 \text{ m/s}^2$)