A pulley is attached to the ceiling of a lift moving upwards. Two particles are attached to the two ends of a string passing over the pulley. The masses of the particles are in the ratio 2 : 1. If the acceleration of the particles relative to the lift is g/2, then the acceleration of the lift will be

All surfaces are assumed to be frictionless. Calculate the horizontal force F that must be applied so that m₁ and m₂ do not move relative to m₃ is :-
                                      

Two masses of 1 kg and 2 kg are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in figure. The masses start moving; during this interval the reading of spring balance will be:-
                                                      

As shown in the figure a monkey of $20 \mathrm{kg}$ mass is holding a light rope that passes over a frictionless pulley. A bunch of bananas of the same mass $20 \mathrm{kg}$ is tied to the other end of the rope. In order to get access to the bananas, the monkey starts climbing the rope. The distance between the monkey and the bananas:-

The same spring is attached with $2 \mathrm{kg}$, $3 \mathrm{kg}$ and $1 \mathrm{kg}$ blocks in three different cases as shown in the figure. If $x_1$, $x_2$ and $x_3$ be the respective extensions in the spring in these three cases, then:-

Two forces ${\overrightarrow{F}}_1=\left(3 \mathrm{N}\right)\hat{\mathrm{i}}-\left(4 \mathrm{N}\right)\hat{\mathrm{j}}$ and ${\overrightarrow{F}}_2=-\left(1 \mathrm{N}\right)\hat{\mathrm{i}}-\left(2 \mathrm{N}\right)\hat{\mathrm{j}}$ act on a point object. In the given figure which of the eight vectors represents ${\overrightarrow{F}}_1$ and ${\overrightarrow{F}}_2$? What is the magnitude of the net forces?

Three blocks of masses $m$, $3m$ and $5m$ are connected by massless strings and pulled by a force $F$ on a frictionless surface as shown in the figure below. The tension $P$ in the first string is $16 \mathrm{N}$.

If the point of application of $F$ is changed as given below, the values of $V$ and $Q^{\text{'}}$ shall be:-