Free Body Diagrams

Q. How many external forces would appear to act on $(m_2+m_3)$ if they are considered as a system and $m_1$ is considered as another system in the figure shown?

1. $1$
2. $2$
3. $3$
4. $4$

Q. The coefficient of friction between the block and the surface is $0.4$ in Fig. (i-iv). Match Column I with Column II.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i. Force of friction is zero in}& \text{a. Fig. (i)}\\ \text{ii. Force of friction is}2.5\text{N in}& \text{b. Fig. (ii)}\\ \text{iii. Acceleration of the block is zero in}& \text{c. Fig. (iiii)}\\ \text{iv. Normal force is not equal to}2\text{g in}& \text{d. Fig. (iv)}\end{array}$

1. $i-b,ii-a,iii-a,b,c,iv-c$
2. $i-b,ii-c,d,iii-d,iv-a,d$
3. $i-a,c,ii-b,d,iii-a,b,c,d,iv-c,d$
4. $i-d,ii-a,b,iii-d,iv-c$

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

Q. Two smooth cylindrical bars weighing $W$ each, lie next to each other in contact. A similar third bar is placed over the two bars as shown in figure. Neglecting friction, the minimum horizontal force on each lower bar necessary to keep them together is

1. $\frac{W}{2}$
2. $W$
3. $\frac{W}{\sqrt{3}}$
4. $\frac{W}{2\sqrt{3}}$

Q. In the figure pulley $p_1$ is fixed and $p_2$
is movable. If $W_1=W_2=100N,$ what is the angle (in degrees) $A{P}_2{P}_1$ when the system is in equilibrium?

The pulleys are massless and frictionless

Q.

Match the block diagrams of block of mass, m, with their corresponding free body diagram.

(Bodies are at rest with respect to ground)

1. P - (i); Q - (iii); R - (iv); S - (ii)

2. P - (ii); Q - (ii); R - (iv); S - (ii)

3. P - (i); Q - (iii); R - (iv); S - (iv)

4. None of these

Q. A man of mass $50\text{kg}$ stands on a frame of mass $30\text{kg}$. 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 $g=10{\text{m/s}}^2$)

1. $400\text{N}$
2. $374\text{N}$
3. $418\text{N}$
4. $448\text{N}$

Q. A rod $\text{AB}$ rests with the end $\text{A}$ on rough horizontal ground such that end $\text{A}$ is prevented from sliding to the right. And the end $\text{B}$ against a smooth vertical wall. The rod is uniform and of weight $W$. If the rod is in a stationary position as shown in figure, the number of forces acting in the FBD of rod is/are ?

1. $1$
2. $2$
3. $3$
4. $4$

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 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.

Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force F = 10 N, , then tension $T_1=$

1. 1N

2. 5N

3. 8N

4. 10N

Q. In the figure pulley $p_1$ is fixed and $p_2$
is movable. If $W_1=W_2=100N,$ what is the angle (in degrees) $A{P}_2{P}_1$ when the system is in equilibrium?

The pulleys are massless and frictionless

Q. You were wondering that while train is running at constant velocity and driver applies brake to stop the train, you always feel a sudden jerk. A scientific answer for this event will be obtained by:

1. Newton's third law of motion
2. Newton's second law of motion
3. Newton's first law of motion
4. Newton's law of gravitation

Q.

Three masses of 15 kg. 10 kg and 5 kg are suspended vertically as shown in the fig. If the string attached to the support breaks and the system falls freely, what will be the tension in the string between 10 kg and 5 kg masses. Take $g=10m{s}^{-2}$ . It is assumed that the string remains tight during the motion

1. 300 N

2. 250 N

3. 50 N

4. Zero

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. Which of the following forces arise due to interaction between electrons/protons or atomic interactions of the bodies in contact with each other?

1. Tension
2. Frictional force
3. Weight of body
4. Both (a) and (b)

Q. A rod AB of weight $W_2$ is placed over a sphere of weight $W_1$ as shown in figure. If friction is absent, the number of forces to be shown on the sphere in its $FBD$ is/are?

1. $3$
2. $4$
3. $5$
4. $6$

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 cylinder weighing $‘W^{\prime }$ is resting on a V-groove as shown in figure. How many forces should be shown in the $FBD$?

1. $1$
2. $2$
3. $3$
4. $4$

Q. Considering the FBD for a block of mass m kg kept on a fixed inclined plane, which of the following statement is true?

1. N will not have any component along inclined plane
2. Block will not move
3. Block will move in a direction perpendicular to inclined plane
4. mg can not be resolved along the inclined plane

Q. In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to the $n^{th}$ mass is

1. $\frac{mMg}{nm+M}$
2. $\frac{mMg}{nmM}$
3. $mg$
4. $nmg$

Q. Statements I: Block $A$ is moving on the horizontal surface towards the right under the action of force $F$. All surfaces are smooth. At the instant shown, the force exerted by block $A$ on block $B$ is equal to the net force on block $B$.
Statement II: From Newton’s Third Law, the force exerted by Block $A$ on Block $B$ is equal in magnitude to force exerted by block $B$ on $A$.

1. Both Statements I and II are true and Statement II is correct explanation of Statement I
2. Both Statements I and II are true but Statement II is not correct explanation of Statement I
3. Statement I is true and statement II is false
4. Statement I is false and statement II is true

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. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. A $50\text{kg}$ person stands on a $25\text{kg}$ platform. He pulls the rope which is attached to the platform through the frictionless pulleys as shown in the figure. If the platform moves upwards at a steady velocity, find the force with which man pulls the rope. Take $g=10{\text{m/s}}^2$.

1. $325\text{N}$
2. $175\text{N}$
3. $250\text{N}$
4. $750\text{N}$

Q. How many forces are acting on $M$ when its $FBD$ is drawn? (Given all surfaces are smooth)

1. $2$
2. $3$
3. $4$
4. $5$

Q. In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to the $n^{th}$ mass is

1. $\frac{mMg}{nm+M}$
2. $\frac{mMg}{nmM}$
3. $mg$
4. $nmg$

Q. If the coefficient of friction between the wedge and the block is $\mu$, then the maximum acceleration of the wedge for which the block will remain at rest with respect to it is

1. $2g\left(\frac{1+\mu }{1-\mu }\right)$
2. $g\left(\frac{1+\mu }{1-\mu }\right)$
3. $g\left(\frac{1-\mu }{1+\mu }\right)$
4. $2g\left(\frac{1-\mu }{1+\mu }\right)$

Q. A $50\text{kg}$ person stands on a $25\text{kg}$ platform. He pulls the rope which is attached to the platform through the frictionless pulleys as shown in the figure. If the platform moves upwards at a steady velocity, find the force with which man pulls the rope. Take $g=10{\text{m/s}}^2$.

1. $325\text{N}$
2. $175\text{N}$
3. $250\text{N}$
4. $750\text{N}$

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

Q. Find the reading of spring balance as shown in figure. Assume that mass $M$ is in equilibrium and all surfaces are smooth.

1. 8 N
2. 9 N
3. 12 N
4. Zero