A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in its natural state. Then the maximum positive work that the applied force $F$ can do is: [Given that spring does not break] 

A block of mass $m$ is placed inside a smooth hollow cylinder of radius $R$ whose axis is kept horizontally. Initially, the system was at rest. Now cylinder is given constant acceleration $2\mathit{ }g$ in the horizontal direction by an external agent. The maximum angular displacement of the block with the vertical is: 

In the figure, a block slides along a track from one level to a higher level, by moving through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block’s initial speed $v_0$ is $6 \mathrm{m} {\mathrm{s}}^{-1}$, the height difference $h$ is $1.1 \mathrm{m}$ and the coefficient of kinetic friction $\mathrm{\mu } \mathrm{is} 0.6.$ The value of $d$ is : 

A small particle slides along a track with elevated ends and a flat central part, as shown in the figure. The flat part has a length $3 \mathrm{m}$. The curved portions of the track are frictionless, but for the flat part, the coefficient of kinetic friction is $\mathrm{\mu } = 0.2.$The particle is released at point $A$, which is at a height $h =1.5 \mathrm{m}$ above the flat part of the track. The position where the particle finally come to rest is: 

A block of mass $50 \mathrm{kg}$ is projected horizontally on a rough horizontal floor. The coefficient of friction between the block and the floor is $0.1.$ The block strikes a light spring of stiffness $k= 100 \mathrm{N} {\mathrm{m}}^{-1}$ with a velocity $2 \mathrm{m} {\mathrm{s}}^{-1}.$ The maximum compression of the spring is:

A $10 \mathrm{kg}$ small block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius $10 \mathrm{m}$. The applied force is of $200 \mathrm{N}$ as shown in the figure. If the block started from rest at $A$, the speed at $B$ would be: $(g = 10 \mathrm{m} {\mathrm{s}}^{-2})$

In the figure the variation of components of acceleration of a particle of mass $1 \mathrm{kg}$ is shown w.r.t. time. The initial velocity of the particle is $\overrightarrow{u}=\left(-3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$.The total work done by the resultant force on the particle in the time interval from $t=0$ to $t=4$ seconds is :