In the figure shown acceleration of monkey relative to the rope if it exerts a force of $80 \mathrm{N}$ on string will be

In the given figure, inclined surface and pulleys are smooth. Strings and pulleys are massless. Acceleration of mass $m$ is

A balloon is tied to a block. The mass of the block is $2 \mathrm{kg}$. The tension of the string between the balloon and the block is $30 \mathrm{N}$. Due to the wind, the string has an angle $\mathrm{\theta }$ relative to the vertical direction. $\mathrm{cos\theta }=\frac{4}{5}$ and $\mathrm{sin\theta }=\frac{3}{5}$. Assume the acceleration of gravity is $g=10 \mathrm{m} {\mathrm{s}}^{-2}$. Also assume the block is small so the force on the block from the wind can be ignored. Then the $x$ - component and the $y$-component of the acceleration of the block is

Find the force exerted by the block on the rod.

As shown to the right, two blocks with masses $m$ and $M(M>m)$ are pushed by a force $F$ in both Case $\mathrm{I}$ and Case $\mathrm{II}$. The surface on which blocks lie, is horizontal and frictionless. Let $R_I$ be the force that $m$ exerts on $M$ in case $\mathrm{I}$ and $R_{II}$ be the force that $m$ exerts on $M$ in

case $\mathrm{II}$. Which of the following statement is true?

Block $A$ of mass $m$ is placed on a plank $B$. A light support $S$ is fixed on plank $B$ and is attached with the block $A$ with a spring of spring constant $K$. Consider that initially spring is in its natural length. Find the maximum compression in the spring, if the plank $B$ is given an acceleration $a$. All the surfaces are smooth 

In figure, two identical particles each of mass $m$ are tied together with an inextensible light string. This is pulled at its centre with a constant force $F$. If the whole system lies on a smooth horizontal plane, then the acceleration of approach of particles towards each other at the instant shown in figure is:

A block of mass $m$ lies on wedge of mass $M,$ which lies on fixed horizontal surface. The wedge is free to move on the horizontal surface. A horizontal force of magnitude $F$ is applied on block as shown, neglecting friction at all surfaces, the value of force $F$ such that block has no relative motion w.r.t. wedge will be : (where $\mathrm{g}$ is acceleration due to gravity)