$A$ car is moving on a circular horizontal track of radius $10 \,m$ with a constant speed of $10 \,m/s$. $A$ bob is suspended from the roof of the car by a light wire of length $1.0 \,m$. The angle made by the wire with the vertical is (in rad)

Three masses $M = 100 \, kg$,$m_{1} = 10 \, kg$,and $m_{2} = 20 \, kg$ are arranged in a system as shown in the figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. $A$ force $F$ is applied on the system so that the mass $m_{2}$ moves upward with an acceleration of $2 \, m/s^{2}$. The value of $F$ is $...... \, N$. (Take $g = 10 \, m/s^{2}$)

$A$ body of mass $50 \ kg$ is suspended using a spring balance inside a lift at rest. If the lift starts falling freely,the reading of the spring balance is:

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

$A$ vessel containing water is given a constant acceleration $a$ towards the right,along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?

$A$ man of mass $70 \; kg$ stands on a weighing scale in a lift which is moving:
$(a)$ Upwards with a uniform speed of $10 \; m s^{-1}$.
$(b)$ Downwards with a uniform acceleration of $5 \; m s^{-2}$.
$(c)$ Upwards with a uniform acceleration of $5 \; m s^{-2}$.
What would be the readings on the scale in each case?
$(d)$ What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?