$A$ man of mass $60 \ kg$ is standing in a lift moving up with a retardation of $2.8 \ ms^{-2}$. The apparent weight of the man is (in $N$)

$A$ ball is suspended on a thread from the ceiling of a car. The brakes are applied and the speed of the car changes from $5 \, m/s$ to $5/3 \, m/s$ during a time interval of $3 \, s$. Find the angle $\theta$ that the thread will deviate from the vertical.

$A$ man weighing $75 \,kg$ is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is

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 $g = 10 \, m/s^{2}$)

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 ..........

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