Free Body Diagrams

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 T1=

1. 1 N

2. 5 N

3. 8 N

4. 10 N

Q.

The free body diagram of a car moving on the banked road is

1. 

2. 

3. 

4. 

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. 5 N

2. 4 N

3. 2 N

4. None of the above

Q.

Two blocks are in contact on a frictionless table one has a mass m and the other 2 m 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 : 2

3. 1 : 3

4. 1 : 4

Q. How many forces would be acting on $M$ when its $FBD$ is considered?

1. $5$
2. $6$
3. $7$
4. $8$

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. A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s¯² The crew and the passengers weigh 300 kg. Give the magnitude and direction of the (a) force on the floor by the crew and passengers, (b) action of the rotor of the helicopter on the surrounding air, (c) force on the helicopter due to the surrounding air.

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. None of these

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

Q. A block of mass 1 kg is kept on incline plane inside lift as shown in figure. If lift starts accelerating up at 2 m/$s^2$ from rest then work done by frictional force in 1 second is (in J)
( g = 10 m/$s^2$)


Friction between block and plane is 0.8.

Q. Two thin and light rods $A$ and $B$ are attached to a block of mass $m$ with the help of a massless string as shown in the figure. Then identify the correct statement, if the angle between the rods is acute.

1. Both $A$ and $B$ experience compression
2. Both $A$ and $B$ experience extension
3. $A$ experiences extension and $B$ experiences compression
4. $B$ experiences extension and $A$ experiences compression

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. 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. Three light strings are connected at the point $P$. A weight $W$ is suspended from one of the strings. End $A$ of string $AP$ and end $B$ of string $PB$ are fixed as shown. In equilibrium, $PB$ is horizontal and $PA$ makes an angle of ${60}^{\circ }$ with the horizontal. If the tension in $PB$ is $30N$, then the tension in $PA$ and weight $W$ are respectively given by

1. $60N,30N$
2. $\frac{60}{\sqrt{3}}N,\frac{30}{\sqrt{3}}N$
3. $60N,30\sqrt{3}N$
4. $60\sqrt{3}N,30\sqrt{3}N$

Q.

Find the friction on B due to A when:-

(i) The wall is smooth but the surfaces of A and B in contact are rough and the system is in equilibrium

(ii) All the surfaces are rough

(p) upward

(q) downwards

(r) zero

(s) system cannot remain in equilibrium

1. (i) - p; (ii) - q

2. (i) - q; (ii) - r

3. (i) - s; (ii) - p

4. (i) - r; (ii) - q

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. If the $10\text{kg}$ and $20\text{kg}$ bodies are considered to be system $1$ and $30\text{kg}$ body is considered as system $2$. The number of forces that would appear to be acting as an external force for system 1 is

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.

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. In the figure shown, a body of mass $6kg$ is at a distance of $16m$ from the pulley at $t=0$ when it is released. If the string is cut after $2s$, then find the time after which the $6kg$ block will hit the pulley. Consider the surface to be smooth (Take $g=10m/s^2$)

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

Q. If the $10\text{kg}$ and $20\text{kg}$ bodies are considered to be system $1$ and $30\text{kg}$ body is considered as system $2$ , how many forces would appear to be acting as external forces for system $1$?

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

Q. The $FBD$ of the frame and the person for the figure shown is

1. 
2. 
3. 
4. 

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

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

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 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. 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. 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. A rigid rod is resting with each end touching against 2 perpendicular rods parallel to the coordinate axes. What will be the direction of the normal force due toj each rod?

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

Q. If the $10\text{kg}$ and $20\text{kg}$ bodies are considered to be system $1$ and $30\text{kg}$ body is considered as system $2$. The number of forces that would appear to be acting as an external force for system 1 is

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. $\frac{g}{5}$