Two bodies of masses $m_1$ and $m_2$ are connected by a light string which passes over a frictionless,massless pulley. If the pulley is moving upward with uniform acceleration $\frac{g}{2}$,then the tension in the string will be .........

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

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

$A$ block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

$A$ 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 $N$)