Inside a horizontally moving box,an experimenter finds that when an object is placed on a smooth horizontal table and is released,it moves with an acceleration of $10\,m/s^2$. In this box,if a $1\,kg$ body is suspended with a light string,the tension in the string in the equilibrium position (with respect to the experimenter) will be $.........\,N$. (Take $g = 10\,m/s^2$)

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

$A$ monkey is sitting on the pan of a spring balance which is placed on an elevator. The maximum reading of the spring balance will be when

$A$ wire is bent into the shape of a parabola given by $Y = Kx^2$. $A$ bead of mass $m$ is placed on the wire,which can slide on it without friction. Initially,when the wire is at rest,the bead is at the lowest point of the parabola. If the wire is now moved with a constant acceleration $a$ parallel to the $X$-axis,what will be the distance of the new equilibrium position of the bead from the $Y$-axis,such that it remains stationary relative to the wire?

If a trolley accelerates horizontally with acceleration $a$,then the bob is displaced backward from its initial vertical position. The angular deflection of the bob in equilibrium is ..........