Wedge-Block System

A weight of $500\mathrm{N}$ is help on a smooth plane, inclined at ${30}^{\mathrm{o}}$ to the horizontal by a force $\mathrm{P}$ acting ${30}^{\mathrm{o}}$ above the plane as shown by the figure. The reaction of the plane on the weight will be:

The co-efficient of friction $\mathrm{\mu }$ and the angle of friction $\mathrm{\theta }$ are related as

A body is resting on a plane inclined at angle ${30}^{\mathrm{o}}$, to horizontal. What force would be required to slide it down, if the co-efficient of friction between body and plane is $0.3$?

A box weight $1000\mathrm{N}$ is placed on the ground. The co-efficient of friction between the box and th ground is $0.5$. When the box is pulled by a $100\mathrm{N}$ horizontal force, the frinctional force developed between the box and ground at imepending motion is 

A block of mass $5\mathrm{kg}$ slides down from rest along a frictionless inclined plane that makes an angle of ${30}^{\mathrm{o}}$ with horizontal. What will be the speed of the  block after it covers a distance of $3.6\mathrm{m}$ along the plane?$\left[\mathrm{g}=10 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.\right]$

A body of mass $m$ is resting on a wedge having inclination $\mathrm{\theta }$ as shown in figure. What is the acceleration $a$ of the wedge such that the mass $m$ just falls freely?

The value of $\text{'}F\text{'}$ for which the system is in equilibrium

In the system shown in figure assume that cylinder remains in contact with the two wedges. The velocity of cylinder is

A system is accelerated upward with an acceleration $5 \mathrm{g}$. The apparent weight of a body of mass $m$ in the system is -

In the given figure, if the velocity of the block $\mathrm{C}$ at a particular instant is $-20 \mathrm{m} {\mathrm{s}}^{-1} \hat{\mathrm{j}}$, then the velocity of the rod (A) at that instant will be : (string is attached to wedge)

A body of mass $5 \mathrm{kg}$ is suspended by a spring balance on an inclined plane as shown in the figure. Measure the force applied on spring balance, 

An ice tube is kept on an inclined plane of angle $30°$. The coefficient of kinetic friction between the block and inclined plane is $\frac{1}{\sqrt{3}}$. What is the acceleration of the block?

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both the sides. The coefficient of friction between the block $A$ and the wedge is 2/3 and that between the block $B$ and the wedge is 1/3 and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

Two blocks of equal masses $m$ are released from the top of a smooth fixed wedge as shown in the figure. The acceleration of the centre of mass of the two blocks is

There is a trolley in which there is a fixed inclined surface on which a smooth block of mass $5 \mathrm{kg}$ is placed. Two horizontal forces of magnitude $F_1$ and $F_2$ are applied on the trolley as shown to keep the trolley at rest. The value of $F_1 - F_2$ is : (Assume there is no friction between the trolley and horizontal ground and $g = 10 \mathrm{m} {\mathrm{s}}^{-2}$)

Masses, $M_1$, $M_2$ and $M_3$ are connected by strings of negligible mass which pass over massless and frictionless pulleys ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ as shown in the figure. The masses move such that the portion of the string between ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ is parallel to the inclined plane and the portion of the string between ${\mathrm{P}}_2$ and $M_3$ is horizontal. The masses $M_2$ and $M_3$ are $4.0 \mathrm{kg}$ each and the coefficient of kinetic friction between the masses and the surfaces is $0.25$. The inclined plane makes an angle of $37°$ with the horizontal and the mass $M_1$ moves downwards with a uniform velocity. Find the tension(in $\mathrm{N}$) in the horizontal portion of the string.
(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, $\sin 37°$$\cong$ $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$)

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