We suggest reading Simple Machines - Class 09 Notes, before having a look at its exercises.

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Group A

Group B

Group C

Group D



Simple Machine - Solutions



Group - A


1. Define simple machine.

Answer: Simple machines are the tools that are simple in construction and make our work easier, faster and more convenient by multiplying, magnifying or transferring our applied force from one point to another.

2. Why are simple machines used?

Answer: Simple machines are used to make our work easier, faster, and more convenient.

3. What is mechanical advantage? Write its formula.

Answer: Mechanical Advantage (MA) is the ratio of load to effort, in a simple machine.
The formula of MA = Load /Effort

4. Why is velocity ratio? Write down its formula.

Answer: The ratio of effort distance to load distance, in a simple machine is called Velocity Ratio (VR).
The formula of VR = Effort distance / Load Distance

5. Define input work and output work. 

Answer: The work done by the user to the machine i.e. Effort x Effort Distance is defined as input work.

The work done by the machine i.e. Load x Load Distance is defined as output work.

6. What is efficiency of a machine?

Answer: The ratio of output work to input work expressed in percentage is called the efficiency of a machine. 

7. What are the factors that affect the efficiency of a simple machine?

Answer: Friction is the main factor that affects the efficiency of a simple machine.

8. How can the efficiency of a simple machine be increased? Write.

Answer: Efficiency of a simple machine is reduced as extra effort is wasted in overcoming frictional force and other forces generated in the machine. For this purpose, lubricants can be used to make the surface of the machine slippery and reduce the loss of effort. Hence, the efficiency of the machine can be increased.

9. What is a perfect machine?

Answer: An ideal or perfect machine is that machine whose efficiency is 100%.

10. What is the relationship among the efficiency, output work and input work of a machine?

Answer: The relationship among efficiency, output work and input work of a machine can be expressed as:

Efficiency = Output Work/Input Work *100%


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11. What is a pulley?

Answer: A pulley is a simple machine, that is a wooden or metallic circular disc having a groove on its circumference through which a rope can pass.

12. Define fixed pulley and a movable pulley.

Answer: A pulley that doesn't move up and down along with the load is defined as fixed pulley.

A pulley that moves up and down along with the load is defined as movable pulley.

13. What is the velocity ratio of a single fixed pulley?

Answer: The velocity ratio of a single fixed pulley is 1.
14. What is the velocity ratio of a single movable pulley and the pulley having more than two wheels?

Answer: The velocity ratio of a single movable pulley is 2 and the pulley having more than two wheels is >2.

15. What is an inclined plane?

Answer: An incline plane is a simple machine having a sloping surface that magnifies our applied effort.

16. What is a wheel and axle?

Answer: A wheel and axle is a simple machine, having two co-axial cylinders of different radii, in which the bigger one is wheel and the smaller one is axle.

17. Give any two examples of wheel and axle.

Answer: Any two examples of wheel and axle are spanner and steering of vehicles.

18. What is moment? Write down its formula.

Answer: Moment is the turning effect produced by the force. 
The formula of moment is Force * Moment arm.

19. What are the two factors that affect the turning effect of force (moment)?

Answer: Two factors that affect the moment are:
i) Effort applied (Force)
ii) Distance of moment arm



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Group - B



1. Write any two differences between mechanical advantage (MA) and velocity ratio (VR).

Answer: Two differences between mechanical advantage and velocity ratio are:


Mechanical advantage Velocity ratio
Mechanical advantage is the number that represents the effort multiplied by the machine. (To avoid copy writing, we used this definition. You can use the definition that's in your book.) Velocity ratio is the distance that the applied effort has to travel as compared to the distance travelled by the load.  (To avoid copy writing, we used this definition. You can use the definition that's in your book.)
It is affected by friction. It is not affected by friction.


2. Derive the relation among MA, VR and efficiency.

Solution:

Derivation of relation among MA, VR and efficiency (η)

We know,
MA = Load / Effort
VR = Effort distance/ Load distance
Output Work = Load * Load Distance
Input Work = Effort* Effort Distance

And,
Efficiency = Output Work/ Input Work * 100%
or, Î· = Load * Load Distance / Effort * Effort Distance * 100%
or, Î·  = Load / Effort * Load Distance / Effort Distance * 100%
or,  Î·= MA * 1/Effort Distance/ Load Distance * 100%
or, Î·  = MA * 1/VR *100%
So, Î· = MA/VR *100%


3. What is meant by the statement that the MA of a simple machine is 3?

Answer: The statement, "MA of a simple machine is 3." means the load is moved three times the effort is applied.

4. What is meant by the saying that the VR of a machine is 5?

Answer: The saying that the VR of a machine is 5 means the distance travelled by the effort is five times the distance travelled by the load.

5. What is meant by the statement that efficiency of a simple machine is 60%?

Answer: Efficiency of a simple machine is 60% means that the machine can convert only 60% of our applied effort into useful work and rest 40% is lost to overcome other forces.

6. What is efficiency? Is it possible to make a perfect machine in our daily life?

Answer: The ratio of output work to input work expressed in percentage of any machine is called efficiency.
No, it is not possible to make a perfect machine in our daily life because the frictional force is generated in every machines that decreases some percentage of efficiency of the machine.

7. What is meant by a practical machine? What is the relation between MA and VR in a practical machine?

Answer: The machine having efficiency less than 100% is meant by a practical machine.
In a practical machine, the relation of MA and VR is MA<VR.

8. Write any two ways to reduce the friction in a machine.

Answer: Two ways to reduce the friction in a machine are:

a. Use lubricants like oil, grease in different parts of the machine.
b. Make the surface of the machine smooth by polishing it.

9. Write any two differences between input work and output work.

Answer: Two differences between input work and output work are as follows:

Input Work Output Work
The work done by the user to the machine is called input work.  The work done by the machine is called output work.
Mathematically, Input Work = Effort * Effort distance Mathematically, Output Work= Load * Load distance

10. Write any two differences between practical machine and ideal machine.

Answer: Any two differences between practical machines and ideal machine are as follows:

Practical Machine Ideal Machine
Machines having efficiency less than 100% are called practical machine. Machines having efficiency equal to 100% are called ideal machine.
In practical machine, MA is always less than VR. In ideal machine, MA is always equal to VR.

11. Write any two differences between fixed pulley and movable pulley.

Answer: Differences between fixed pulley and movable pulley are as follows:

Fixed Pulley Movable Pulley
Fixed pulley is that pulley system in which the pulley doesn't move up and down with load.  Movable pulley is that pulley system in which the pulley moves up and down with load.
The MA and VR of fixed pulley is always equal to 1.  The MA and VR of a movable pulley is always greater than 1.


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12. The MA and VR of pulley increases on increasing the number of pulleys in the system. Why?

Answer: In a pulley system, when number of pulleys are added, the length of the rope increases. Hence, the effort has to travel more distance to overcome the load (VR). Similarly, the effort applied also gets reduced as the force is multiplied (MA). So, the MA and VR of pulley increases on increasing the number of pulleys in the system. 

13. The efficiency of a machine can be increased by applying oil or grease. Give reason.


Answer: Friction is less in slippery surfaces. One of the main reason for the reduction of efficiency of a simple machine is production of friction in the machine. On applying oil or grease, the machine parts become slippery and produce less friction. Hence, the efficiency of a machine can be increased by applying oil or grease.

14. Give reason:

a) Scissors and pulleys are called simple machines.

Answer: Scissors and pulleys are simple in construction, easy to use and convenient. Both of them transfer effort from one point to another and make our work easier. So, scissors and pulleys are called simple machines.

b) Mechanical Advantage has no unit.

Answer: Mechanical Advantage is the ratio of Load to Effort. Both load and effort are forces and the units cancel each other. Therefore, mechanical advantage has no unit.

15. Mechanical advantage is always less than velocity ratio in a practical machine, why?

Answer: In a practical machine, efficiency is always less than 100%. Also, MA is affected by friction in those machines while VR is not affected. Therefore, mechanical advantage is always less than velocity ratio in a practical machine.

16. The VR of a single movable pulley is 2. Give reason.

Answer: VR of pulleys depend on the number of rope segments used to support the load. Since two ropes are used in this pulley i.e. the distance travelled by effort is twice the distance travelled by load, the VR of a single movable pulley is 2.

17. The efficiency of a machine cannot be 100%. Give reason.

Answer: Efficiency of a machine depends on MA and VR. MA is affected by friction in real practice whereas VR is not. So, the ratio of MA to VR expressed in percentage (efficiency) is not equal to 100%. Hence, the efficiency of a machine cannot be 100%.

18. Wheel and axle is also called a continuous lever, why?

Answer: Wheel and axle is called a continuous lever because like a lever, it has load, effort and fulcrum. Also, we need to continuously apply effort until the load gets overcomed.

19. The probability of breaking the branch of a tree is more as we move to the top. Give reason.

Answer: The branch of a tree generates moment when we are sitting or standing on the branch. As we move towards the top, the effort arm of the moment increases thus, increasing the turning effect (moment). So, the probability of breaking the branch of a tree is more as we move to the top.

20. A long spanner is used to open the rusted nut, why?

Answer: A long spanner is used to open the rusted nut because large moment is required to open such nuts. And large moment can be produced by increasing the length of the spanner. 

21. The door handles are kept near the edges of the door planks, why?

Answer: The door is relatively easier to open when the door handles are kept near the edges of the door planks because this generates larger turning effect as a result of increased effort arm.

22. The steering wheel of a truck is larger than that of a car. Give reason.

Answer: A truck is a larger vehicle than the car. It requires more moment than a car requires. Hence, to produce larger moment in a truck, the steering wheel of a truck is larger than that of a car.



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Group - C



1. Write any three applications of simple machines in our daily life.

Answer: Three applications of simple machines in our daily life are:

1. They help to multiply our force.
2. They help to change the direction of applied force.
3. They help to increase the speed of doing work.


2. How is MA, VR and efficiency of a wheel and axle calculated? Explain.

Answer: The following figure describes the structure of wheel and axle:

Wheel and axle

To calculate the MA, we have the formula MA = Load/ Effort.

To calculate the VR, we have the formula VR = R/r, where 'R' stands for the radius of the wheel and 'r' stands for the radius of the axle.

To calculate efficiency, we have the formula Efficiency = MA/VR *100%

3. Calculate the efficiency of a lever if its MA and VR are 3 and 4 respectively.

Solution:
Given,
MA of a lever = 3
VR of the lever = 4
Now,

Efficiency of the lever = MA/VR *100%
= 3/4 *100%
= 75%

Hence, the efficiency of the lever is 75%.

4. Calculate the efficiency of a four wheeled pulley system if it is used to lift a load of 500N by using an effort of 300N.

Solution:
Given,
The given pulley system has four puelly, so, VR = 4.
Load (L) = 500N
Effort (E) = 300N

Now,
MA = L/E
= 500/300
= 1.67

And,
Efficiency of the machine = MA/VR * 100%
= 1.67/4 *100%
= 41.67%

Hence, the efficiency of the pulley system is 41.67%.

5. A 20cm long spanner is used to open a rusted nut of a motor cycle by applying an effort of 60N. Calculate the moment produced.

Solution:
Given,
Length of the spanner (r) = 20cm
= 20/100m
= 0.2m
Effort applied (F) = 60N

Now,
Moment = F*r
= 60*0.2
= 12 Nm

Hence, the moment produced is equal to 12Nm.

6. A 25cm long spanner is used to open a rusted nut. If the moment produced is 8Nm, calculate the effort applied.

Solution:
Given,
Length of the spanner (r) = 25cm
= 25/100
= 0.25m
Moment produced = 8Nm

Now,
Moment = F *r
or, 8 = F *0.25
So, F = 32N

Hence, 32N effort was applied to produce 8Nm moment.


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Group - D


1. In a wheel and axle, the radius of the wheel is 50cm and that of the axle is 20cm. If a load of 2000N is lifted by applying an effort of 1000N, calculate MA, VR and Î·.

Solution:
Given,
Radius of wheel (R) = 50cm
Radius of axle (r) = 20cm
Load (L) = 2000N
Effort (E) = 1000N

Now,
MA = L/E
= 2000/1000
= 2

And,
VR = R/r
= 50/20
= 2.5

So, 
η = MA/VR *100%
= 2/2.5*100%
= 80%

Hence, the MA of the wheel and axle is 2, VR is 2.5 and efficiency is 80%.

2. In an inclined plane, an effort is applied to lift a load of 1000N. The MA and VR of that inclined plane is 2 and 3 respectively. Calculate the efficiency and effort applied.

Solution:
Given,
In an inclined plane,
Load (L) = 1000N
MA = 2
VR = 3

Now,
Efficiency of the inclined plane = MA/VR*100%
= 2/3*100%
= 66.67%

And,
MA = L/E
or, 2 = 1000/E
or, E = 1000/2
So, E = 500N

Hence, the efficiency of the inclined plane is 66.67% and the effort applied is 500N.

3. Calculate MA, VR and efficiency when Load is 450N and Effort is 300N in a single movable pulley.

Solution:
Given,
In a single movable pulley,
VR = 2
Load (L) = 450N
Effort (E) = 300N

Now,
MA = L/E
= 450/300
= 1.5

And,
Efficiency = MA /VR *100%
= 1.5/2*100%
= 75%

Hence, the VR of the pulley is 2, MA is 1.5 and efficiency is 75%.


4. Calculate MA, VR and efficiency of an inclined plane whose height is 8 m and length is 32m. Also, load is 1200 N and effort applied is 400N.

Solution:
Given,
Length of the inclined plane (l) = 32m
Height of the inclined plane (h) = 8m
Load (L) = 1200N
Effort (E) = 400N

Now,
MA = L/E
= 1200/400
= 3

And,
VR = l/h
= 32/8
= 4

So,
Efficiency = MA /VR *100%
= 3/4*100%
= 75%

Hence, the MA of the incline plane is 3, VR is 4 and the efficiency is 75%.

5. Although there is no gain in MA and VR, yet single fixed pulley is widely used. Give two reasons to justify this statement. Draw a neat and labelled figure a wheel and axle.

Answer: Although, there is no gain in MA and VR, yet single fixed pulley is widely used because of the following reasons:

a. It transfers our applied effort from one point to another and makes it easy to lift the smaller load.
b. The load can be lifted by a person's by applying effort downwards while using their own body weight.

The neat and well-labelled figure of a wheel and axle is shown here.


If you haven't already looked the notes Simple Machines - Class 09 Notes, have a look at it.

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