A block of mass m is lying at rest on an inclined plane having angle of inclination explain the equilibrium of the block by showing various forces acting on it.

A block of mass $5 \mathrm{kg}$ is kept against an accelerating wedge with a wedge angle of $45°$ to the horizontal. The co-efficient of friction between the block and the wedge is $\mu =0.4$. What is the minimum absolute value of the acceleration of the wedge to keep the block steady. Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$

A log of mass $200 \mathrm{kg}$ is dragged up a slope at an angle of $13°$ to the horizontal by a rope attached to a truck. The rope is at an angle of $20°$ above the slope.

Draw the force diagram for this situation.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

A ball of mass $3 \mathrm{kg}$ is rolled with initial speed $4 \mathrm{m}{ \mathrm{s}}^{-1}$ up a slope at an angle $10°$ to the horizontal.

Find the maximum distance up the slope the ball reaches.

A $10 \mathrm{m}$ long slope makes an angle $30°$ with the horizontal. $A$ box of mass $8 \mathrm{kg}$ is pulled up the slope by a rope that is parallel to the slope. The coefficient of friction between the box and the slope is $\frac{1}{\sqrt{12}}.$ At the top of the slope, the rope passes over a smooth pulley. A ball of mass $12 \mathrm{kg}$ hangs from the other end of the rope. The ball is initially $2 \mathrm{m}$ above the ground. The system is released from rest.

Find how long it will take for the box to travel $1.5 \mathrm{m}$ up the slope.

A block of mass $60 \mathrm{kg}$ is pulled up a hill in the line of greatest slope by a force of magnitude $50 \mathrm{N}$ acting at an angle $\alpha °$ above the hill. The block passes through points $A$ and $B$ with speeds $8.5 \mathrm{m}{ \mathrm{s}}^{-1}$ and $3.5 \mathrm{m}{ \mathrm{s}}^{-1}$ respectively (see diagram). The distance $AB$ is $250 \mathrm{m}$ and $B$ is $17.5 \mathrm{m}$ above the level of $A.$ The resistance to motion of the block is $6 \mathrm{N}.$ Find the value of $\alpha .$

Particles $A$ and $B,$ each of mass $0.5 \mathrm{kg},$ are attached to the ends of a light inextensible string. Particle $A$ is held on a smooth slope inclined at $30°$ to the horizontal. The string passes over a small smooth pulley at the top of the slope and particle $B$ hangs vertically below the pulley. Particle $A$ is released and moves up the slope.Particle $B$hits the ground after $1.2 s$ It then stays on the ground and particle $A$ travels further up the slope. Particle A does not reach the pulley in the subsequent motion.

Find the acceleration of particle $A$ up the slope. 

Particles $A$ and $B,$ each of mass $0.5 \mathrm{kg},$ are attached to the ends of a light inextensible string. Particle $A$ is held on a smooth slope inclined at $30°$ to the horizontal. The string passes over a small smooth pulley at the top of the slope and particle $B$ hangs vertically below the pulley. Particle $A$ is released and moves up the slope.Particle  $B$ hits the ground after$1.2 \mathrm{s}$  It then stays on the ground and the particle $A$ travels further up the slope. Particle $A$ does not reach the pulley in the subsequent motion.

Find the distance travelled by particle $A,$ from when it is released to when it comes to instantaneous rest.

A ball of mass $3 \mathrm{kg}$ is rolled with initial speed $4 \mathrm{m}{ \mathrm{s}}^{-1}$ up a slope at an angle $10°$ to the horizontal.

What assumptions have been made to answer the question?