Free Body Diagrams

Q.

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move?

1. $20\text{N}$
2. $10\text{N}$
3. $12\text{N}$
4. $15\text{N}$

Q.

A rocket has been fired upwards to launch a satellite in its orbit. Name the two forces acting on the rocket immediately after leaving the launching pad.

Q. A horizontal force $F$ is applied at the center of mass of a cylindrical object of mass $m$ and radius $R$, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $\mu$. The center of mass of the object has an acceleration $a$. The acceleration due to
gravity is $g$. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?

1. For the same $F$, the value of $a$ does not depend on whether the cylinder is solid or hollow.
2. For a solid cylinder, the maximum possible value of $a$ is $2\mu g$
3. The magnitude of the frictional force on the object due to the ground is always $\mu mg$
4. For a thin-walled hollow cylinder, $a=\frac{F}{2m}$

Q. Find the acceleration of the block of mass $M$ in the situation shown in the figure. All the surfaces are frictionless and the pulley and the string are light.

1. $g$
2. $\frac{g}{3}$
3. $3g$
4. $\frac{g}{5}$

Q. The pulleys and strings shown in the figure are smooth and massless. For the system to remain in equilibrium, the angle $\theta$ should be:

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q. A particle of mass 1 Kg and carrying 0.01 C is at rest on an inclined plane of angle ${30}^{\circ }$ with horizontal when an electric field of $\frac{490}{\sqrt{3}}N{C}^{-1}$ applied parallel to horizontal, the coefficient of friction is

1. $0.5$
2. $\frac{1}{\sqrt{3}}$
3. $\frac{\sqrt{3}}{7}$
4. $\frac{\sqrt{3}}{2}$

Q. A body of mass $m$ is launched up on a rough inclined plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$ if the time of ascent is half of the time of descent. The value of $x$ is ______.

Q. A man of mass $50kg$ stands on a frame of mass $30kg$. He pulls on a light rope which passes over a pulley. The other end of the rope is attached to the frame. For the system to be in equilibrium, what force must the man exert on the rope? (Take $g=10m/s^2$)

1. $400N$
2. $800N$
3. $300N$
4. $500N$

Q.

Two blocks are in contact on a frictionless table masses $2m$ and $m$ respectively as shown in figure. Force F is applied on mass $2m$ then system moves towards right. Now the same force F is applied on $m$. The ratio of force of contact between the two blocks will be in the two cases respectively.

1. 1 : 1

2. 1 : 4

3. 1 : 2

4. 1 : 3

Q. A $50kg$ homogeneous smooth sphere rests on the ${30}^{\circ }$ inclined plane $A$ and bears against the smooth vertical wall $B$ . The contact force at point $B$ is
(Take $g=10m/s^2$)

1. $250N$
2. Zero
3. $\frac{500}{\sqrt{3}}N$
4. $500N$

Q. A motorcycle is going on an overbridge of radius R . The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it

1. Increases
2. Decreases
3. Remains the same
4. Fluctuates

Q. Three blocks $A,B,$ and $C$ are suspended as shown in figure. Mass of block $A$ and $B$ is $m$ each. If the system is in equilibrium and mass of $C$ is $M$, then

1. $M\ge 2m$
2. $M=2m$
3. $M\le 2m$
4. None of these

Q. Find the contact force between the $3kg$ and $2kg$ block as shown in the figure.

1. $75N$
2. $25N$
3. $55N$
4. $45N$

Q. A rod $AB$ is shown in figure. End $A$ of the rod is fixed on the ground. Block is moving with velocity $\sqrt{3}\text{m/s}$ towards right. The velocity of end $B$ of rod when rod makes an angle of ${60}^{\circ }$ with the ground is

1. $\sqrt{3}\text{m/s}$
2. $2\text{m/s}$
3. $2\sqrt{3}\text{m/s}$
4. $3\text{m/s}$

Q. The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be:

1. $0^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${30}^{\circ }$

Q. An infinitely long string uniformly charged with a linear charge density ${\lambda }_1$ and a segment of length uniformly charged with linear charge density ${\lambda }_2$ lie in a plane at right angles to each other and are separated by a distance $r_0$ as shown in figure. The force with which these two interact is $\frac{{\lambda }_1{\lambda }_2}{4\pi {ϵ}_0}\ln \left(x\right)$, then find the value of $x$ , if $l=r_0$.

Q.

Two blocks of mass 4 kg and 6 kg are placed in contact with each other on a frictionless horizontal surface. If we apply a push of 5 N on the heavier mass, the force on the lighter mass will be

1. 2 N

2. None of the above

3. 5 N

4. 4 N

Q.

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. A vertical force of magnitude $100N$ is applied at point $A$ of the frame. Suppose the force is resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ________. $[$Given: $\sin 35°=0.573$, $\cos 35°=0.819$, $\sin 110°=0.939$, $\sin 110°=-0.342]$

Q.

What do you understand by inter atomic forces.

Q. A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination ${30}^{\circ }$ with horizontal. Acceleration of train up the plane is $a=\frac{g}{2}$. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is $\theta$. Then $\tan \theta$ upto 2 decimal places is

Q. A $20\text{kg}$ floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in figure. A cable at an angle of ${30}^{\circ }$ with the beam helps to support the light. The tension in the cable is

Q. 19.One end of a uniform rod of mass M and length L is clamped. The rod lies on a smooth horizontal surface and rotates on it about the clamped end at a uniform angular velocity Omega. The force exerted by the clamp on the rod has a horizontal component?

Q. An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitude of $F_1$ and $F_2$ (in N).

1. $4\sqrt{3}$ and $\frac{20}{\sqrt{3}}$
2. $\frac{4}{\sqrt{3}}$ and $20\sqrt{30}$
3. $4\sqrt{3}$ and $20\sqrt{3}$
4. $\frac{4}{\sqrt{3}}$ and $\frac{20}{\sqrt{3}}$

Q. Find the normal reaction at the contact points of sphere with walls.


Consider $N_1$ and $N_2$ to be the normal reactions by first and second wall respectively. [ Take $g=10{\text{m/s}}^2$ ]

1. $N_1=25\sqrt{3}\text{N},N_2=50\sqrt{3}\text{N}$
2. $N_1=N_2=\frac{100}{\sqrt{3}}\text{N}$
3. $N_1=N_2=\frac{100}{\sqrt{2}}\text{N}$
4. $N_1=\frac{25}{\sqrt{3}}\text{N},N_2=\frac{100}{\sqrt{3}}\text{N}$

Q. Find the contact force between the $3kg$ and $2kg$ block as shown in the figure.

1. $75N$
2. $25N$
3. $55N$
4. $45N$

Q. In the given diagram, with what force must the man pull the rope to hold the plank in position? $($Mass of the man is $80k$; neglect the weight of the plank, rope and pulley; take $g=10{m/s}^2)$

1. $200N$
2. $300N$
3. $600N$
4. $150N$

Q. An iron nail is dropped from a height h from the level of a sand bed. If it penetrates through a distance x in the sand before coming to rest, the average force exerted by the sand on the nail is,

1. 
2. 
3. 
4. 

Q. If the coefficient of friction between all surfaces is $0.4$ then find the minimum force $F$ applied to have system in equilibrium.

1. $72.5\text{N}$
2. $82.5\text{N}$
3. $62.5\text{N}$
4. $92.5\text{N}$

Q. An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitude of $F_1$ and $F_2$ (in N).

1. $4\sqrt{3}$ and $20\sqrt{3}$
2. $\frac{4}{\sqrt{3}}$ and $\frac{20}{\sqrt{3}}$
3. $4\sqrt{3}$ and $\frac{20}{\sqrt{3}}$
4. $\frac{4}{\sqrt{3}}$ and $20\sqrt{30}$

Q. A block P of mass m is placed on smooth horizontal surface and connected with a spring. Another block Q of same mass is placed on the block P. The two blocks are pulled by a distance A and released. The blocks oscillates without slipping on each other. Then match the matrix.

$\begin{array}{cc}\text{(A) Friction force on the block Q when both the}& \text{(P) towards right}\\ \text{blocks coming towards equilibrium position from left is}& \\ \text{(B) Friction force on the block Q when both blocks are going}& \text{(Q) towards left}\\ \text{right from equilibrium position is(exclude the equilibrium position)}& \\ \text{(C) Friction force will be maximum on Q}& \text{(R) at the equilibrium position}\\ \text{(D) Friction force on P when both blocks are coming towards}& \text{(S) at the extreme position}\\ \text{the equilibrium position from right is}& \\ & \text{(T) none of these}\end{array}$

1. A-P; B-Q; C-S; D-P
2. A-Q; B-P; C-S; D-T
3. A-P; B-Q; C-R; D-T
4. A-T; B-Q; C-S; D-R