Draw the $\mathrm{FBD}$ for the following individual parts of the systems:

 

 

 

  

A block of mass $m$ is placed on ground and an additional force $F=mg$ is applied on the block as shown in the figure. Calculate contact force between ground and block.

Two blocks of masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are placed on the ground as shown in the figure. Two forces of magnitude $\mathrm{F}$ act on ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ in opposite directions.

(i) Draw $\mathrm{F}.\mathrm{B}.\mathrm{D}.$ of masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$.

(ii) Calculate the contact force between ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$.

(iii) What will be the value of normal force between ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$.

(iv) Calculate force exerted by ground surface on mass ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$

A sphere of mass $m$, radius $R$ placed between two vertical walls having separation $d$ which is slightly greater than $2R$:

(i) Calculate force exerted by walls on the sphere.

(ii) Calculate force exerted by ground surface on the sphere.

A spherical ball of mass $m=5 \mathrm{kg}$ rests between two planes which make angles of ${30}^{\circ }$ and ${45}^{\circ }$, respectively, with the horizontal. The system is in equilibrium. Find the normal forces exerted on the ball by each of the planes. The planes are smooth.

A one meter long massless string fixed with a wall is pulled horizontally by applying a force of magnitude $10 \mathrm{N}$. Calculate:

(a) the tension at a point $0.5 \mathrm{m}$ away from wall, 

(b) the tension at a point $0.75 \mathrm{m}$ away from wall, 

(c) force exerted by string on the rigid support.

A block of mass $1 \mathrm{kg}$ is suspended by a string of mass $1 \mathrm{kg}$, length $1 \mathrm{m}$ as shown in the figure $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$. Calculate:

(a) the tension in string at its lowest point, 

(b) the tension in string at its mid-point, 

(c) force exerted by support on string.

A block of mass $0.3 \mathrm{kg}$ is suspended from the ceiling by a light string. A second block of mass $0.2 \mathrm{kg}$ is suspended from the first block through another string. Find the tensions in the two strings. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Two unequal masses $m_1$ and $m_2$ are connected by a string going over a clamped light smooth pulley as shown in figure $m_1=3 \mathrm{kg}$ and $m_2=6 \mathrm{kg}$. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds. (b) Find the tension in the string. (c) Find the force exerted by the clamp on the pulley. $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$