Last Updated on April 2, 2025 by XAM CONTENT
Hello students, here you will find numerical on force and laws of Motion with answers. Before we start solving the numerical, let’s see some important points and formulae. This will help you to solve the problems efficiently.
| Topic | Force and Laws of Motion |
| Type of Questions | Numerical Problems |
| Nature of Questions | Formula Based |
| Board | CBSE |
| Class | 9 |
| Subject | Science – Physics |
| Useful for | Class 9 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| FAQ | Provided |
| Important Link | Class 9 Physics Topicwise Numerical Problems |
Understanding Force and Laws of Motion
Force and the laws of motion are fundamental concepts in physics that help us understand how objects move and interact. Here’s a brief explanation to lay the foundation for solving numerical problems:
What is Force?
Force is a push or pull that acts on an object due to its interaction with another object. It can change the object’s state of motion, direction, or shape. Force is a vector quantity, meaning it has both magnitude and direction, and is measured in newtons (N). The formula for force is:
$$
F=m a
$$
Where:
– $F$ is the force (in newtons),
– $m$ is the mass of the object (in kilograms),
– $a$ is the acceleration (in meters per second squared).
Newton’s Laws of Motion
- First Law (Law of Inertia): An object will remain at rest or continue to move in a straight line at constant velocity unless acted upon by an external force. This explains why objects resist changes to their motion.
- Second Law: The force acting on an object is directly proportional to the product of its mass and acceleration. This law forms the basis for solving numerical problems and is mathematically expressed as: F=ma
- Third Law: For every action, there is an equal and opposite reaction. This means forces always occur in pairs, acting on different objects.
The rate of change of momentum of a body is proportional to the applied force and this change in momentum occurs in the direction of the applied force.
In the below section, we are providing numerical problems on Force and Laws of Motion for Class 9 Physics.
Numerical Problems on Force and Laws of Motion with Answers
Formula used:
Units used:
SI unit of force is newton (N).
SI unit of momentum is kg.m/s
Numerical Problem 1:
The mass of a cannon is 500 kg and it recoils with a speed of 0.25 m/s. What is the momentum of the cannon?
Difficulty Level: Easy
Check Answer
Momentum
= m × v
= 500 × 0.25
= 125 kg·m/s
Numerical Problem 2:
2 balls have masses of 50 gm and 100 gm and they are moving along the same line in the same direction with velocities of 3 m/s and 1.5 m/s respectively. They collide with each other and after the collision, the first ball moves with a velocity of 2.5 m/s. Calculate the velocity of the other ball after collision.
Difficulty Level: Medium
Check Answer
Solution:
\( m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \)
\( (0.05 \times 3) + (0.1 \times 1.5) = (0.05 \times 2.5) + (0.1 \times v_2) \)
\( \frac{150}{1000} + \frac{150}{1000} = \frac{125}{1000} + \frac{100 v_2}{1000} \)
\( \frac{300}{1000} = \frac{125 + 100 v_2}{1000} \)
\( 300 = 125 + 100 v_2 \)
\( 100 v_2 = 175 \)
\( v_2 = \frac{175}{100} \)
\( v_2 = 1.75 \, \mathrm{m/s} \)
Numerical Problem 3:
An object of mass 16 kg is moving with an acceleration of 3 m/s2. Calculate the applied force. If the same force is applied on an object of mass 24 kg, how much will be the acceleration?
Difficulty Level: Medium
Check Answer
Solution:
\( F_1 = m_1 \times a_1 \)
\( F_1 = 16 \times 3 \)
\( F_1 = 48 \, \mathrm{N} \)
\( F_2 = m_2 \times a_2 \)
\( a_2 = \frac{F_2}{m_2} \)
\( a_2 = \frac{48}{24} \)
\( a_2 = 2 \, \mathrm{m/s}^2 \)
Numerical Problem 4:
A bullet has a muzzle velocity of 300 m/s. The gun of mass 3 kg has a recoil velocity of ‘v’. Calculate ‘v’. Mass of the bullet is 30 grams.
Difficulty Level: Medium
Check Answer
Ans. 3 m/sNumerical Problem 5:
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate: (i)Velocity acquired by the body. (ii) Change in momentum of the body.
Difficulty Level: Medium
Check Answer
Ans. (i) 15 m/s (ii) 30 kg m/sNumerical Problem 6:
If the momentum of a body of mass 10 kg is 20 kg m/s, find its velocity.
Difficulty Level: Easy
Check Answer
Ans. 2 m/sNumerical Problem 7:
A body of mass 5 kg moves with an acceleration of 4 m/s2. Calculate its change in momentum in 3 seconds.
Difficulty Level: Medium
Check Answer
Ans. 60 kg m/sNumerical Problem 8:
A body of mass 5 kg moves with an acceleration of 2 m/s2. Find the change in momentum of the body in 2 seconds.
Difficulty Level: Medium
Check Answer
Ans. 20 kg m/sConcept Checklist Before Solving Numerical Problems
- I understand all three Newton’s Laws of Motion
- I know the formula F = ma and how to apply it
- I can differentiate between mass and weight
- I can calculate acceleration from given velocity/time
- I am familiar with the concept of momentum
- I can convert all values to the SI unit system (kg, m/s²)
- I understand when a force is positive or negative
- I know how to find net force when multiple forces act on a body
Problems for Practice
Easy Level
Q1. Riya pushes a shopping cart of mass 20 kg with a force of 60 N. Calculate the acceleration of the cart.
Q2. A football of mass 0.5 kg is rolling with a velocity of 3 m/s. What is its momentum?
Q3. A boy applies a force of 25 N on a 5 kg box. What is the acceleration produced in the box?
Q4. An empty cart of mass 10 kg is pulled with a force of 50 N. Find its acceleration.
Q5. A body of mass 8 kg is moving at a uniform velocity of 6 m/s. What is its momentum?
Moderate Level
Q6. A cyclist of mass 60 kg increases his speed from 5 m/s to 15 m/s in 10 seconds. Calculate the force applied.
Q7. A 1500 kg car slows down from 20 m/s to 5 m/s in 5 seconds due to brakes. Calculate the braking force.
Q8. A boy kicks a ball of mass 0.3 kg, changing its velocity from 2 m/s to 10 m/s in 0.5 s. Find the force applied.
Q9. A 4 kg trolley is pulled with a force of 30 N, but there is a frictional force of 6 N. Find the net acceleration.
Q10. A bullet of mass 0.05 kg moving at 400 m/s is brought to rest in 0.01 s by a wall. Calculate the force exerted by the wall.
Q11. A girl running at 6 m/s jumps on a stationary cart of mass 20 kg. If her mass is 40 kg, find the velocity of the cart and the girl after the jump.
Q12. A 500 g ball hits a wall with 10 m/s and rebounds with the same speed. Find the change in momentum.
Q13. A stone of mass 1.5 kg is thrown with a velocity of 12 m/s. Calculate its momentum.
Q14. A motorbike of mass 300 kg accelerates from 10 m/s to 25 m/s in 4 s. Calculate the force produced by the engine.
Q15. A boy pushes a lawn roller of mass 60 kg with a force of 180 N. Calculate the acceleration of the roller.
Q16. A 700 kg car moves with a velocity of 20 m/s. Find its momentum.
Q17. A worker pulls a cart of mass 80 kg with a force of 200 N along a rough road. If friction offers 40 N resistance, find the acceleration.
Q18. A car of mass 1000 kg takes 5 seconds to slow down from 15 m/s to 5 m/s. Calculate the force applied by the brakes.
Q19. A man applies a force of 400 N on a log of wood. If the log has a mass of 200 kg, find its acceleration.
Q20. A 2 kg stone is dropped from a height. Just before hitting the ground, its velocity is found to be 10 m/s. Calculate its momentum.
Tough Level
Q21. During a science exhibition, Aryan builds a launcher that fires a 0.05 kg marble at 40 m/s. If the launcher has a mass of 2 kg, what is the recoil velocity of the launcher?
Q22. In a tug of war, team A applies a force of 600 N and team B applies a force of 580 N. What is the net force and direction of motion of the rope if the mass of the rope is 10 kg?
Q23. A rocket ejects 0.1 kg of gas per second with a velocity of 500 m/s. What is the thrust force generated by the rocket?
Q24. A student runs and jumps onto a skateboard of mass 3 kg. If the student’s mass is 45 kg and initial speed is 4 m/s, find the final speed after jumping on the skateboard.
Q25. A car of mass 1200 kg moving at 30 m/s hits a stationary truck of 3000 kg. If both stick together after collision, calculate their common velocity.
Q26. A spring gun of mass 1.5 kg fires a bullet of 0.05 kg at 200 m/s. Find the recoil velocity of the gun.
Q27. A moving bus suddenly stops, causing passengers to jerk forward. Explain with Newton’s laws and calculate the force on a 60 kg passenger if the bus decelerates at 4 m/s².
Q28. Two skaters, 50 kg and 70 kg, push away from each other. If the lighter skater moves with a speed of 3 m/s, what is the speed of the heavier skater?
Q29. In a physics experiment, a ball of 0.2 kg rebounds from a wall with equal speed after hitting it at 6 m/s. Find the impulse exerted by the wall.
Q30. A boy jumps off a stationary boat of mass 200 kg with a velocity of 5 m/s. If the boy’s mass is 50 kg, what is the velocity of the boat after the jump?
Concept Booster: Common Mistakes
- Confusing mass and weight
- Using incorrect or mixed units
- Forgetting to convert g = 9.8 m/s² when needed
- Misidentifying acceleration as velocity
- Ignoring negative sign for retardation or opposing force
Helpful Links for CBSE Class 9 Science Preparation
- Download Latest Sample Papers for CBSE Class 9 Science
- Download Worksheets for CBSE Class 9 Science
- Download Chapter Tests for CBSE Class 9 Science
- Download Case Study Question Bank for CBSE Class 9 Science
- Download Numerical Problems for CBSE Class 9 Physics
- Download Important MCQs for CBSE Class 9 Physics
Frequently Asked Questions (FAQs) on Force and Laws of Motion Numerical Problems
Q1: What is force?
A1: Force is a push or pull acting on an object as a result of its interaction with another object. It can change the object’s state of motion, direction, or shape. Force is measured in newtons (N) and is a vector quantity, meaning it has both magnitude and direction.
Q2: How do numerical problems prepare students for exams?
A2: Numerical problems prepare students for exams in several ways:
Practice and Familiarity: Regular practice with numerical problems makes students familiar with the types of questions they may encounter in exams.
Time Management: Solving numerical problems helps students develop the ability to manage their time effectively during exams.
Confidence Building: Successfully solving numerical problems boosts confidence, reducing exam anxiety.
Error Identification: It helps students identify common mistakes and learn from them, improving accuracy in exams.
Q3: Why are numerical problems useful for understanding physics?
A3: Numerical problems are useful for understanding physics because:
Practical Application: They allow students to apply theoretical knowledge to practical situations, enhancing understanding.
Critical Thinking: They encourage critical thinking and logical reasoning, essential for comprehending physical phenomena.
Interconnected Concepts: They demonstrate how different concepts in physics are interconnected, providing a holistic understanding.
Visualization: They often involve diagrams and visual aids, helping students visualize and grasp abstract concepts better.
Q4: What are the key steps to solve numerical problems on force and laws of motion?
A4: The key steps to solve numerical problems on force and laws of motion are:
Read the Problem Carefully: Understand the given data and what is being asked.
Identify the Known and Unknown Variables: List out the known quantities and what needs to be calculated.
Select the Appropriate Formula: Choose the correct formula based on the known and unknown variables.
Perform the Calculations: Substitute the known values into the formula and solve for the unknown.
Check the Units: Ensure the units are consistent and convert them if necessary.
Review the Answer: Check if the answer is reasonable and verify it with the context of the problem.
Q5: What tips can help students improve their skills in solving numerical problems?
A5: Here are some tips to improve skills in solving numerical problems:
Practice Regularly: Consistent practice is key to mastering numerical problems.
Understand the Concepts: Ensure a strong grasp of the underlying concepts before attempting problems.
Review Mistakes: Learn from errors by reviewing and understanding where you went wrong.
Q6: Are there any online resources for practicing numerical problems on force and laws of motion?
A6: Yes, there are several online resources available for practicing numerical problems, including:
Educational Websites: Websites like Physics Gurukul offer practice problems and tutorials.
xamcontent.com: Xam Content also offers numerical problems on different topics for all classes.
Q7: What is momentum?
A7: Momentum is the product of an object’s mass and its velocity. It is a vector quantity and is given by, p = mv. The SI unit of momentum is kg·m/s.
Q8: What is the SI unit of force?
A8: The SI unit of force is the newton (N). One newton is the force required to accelerate a 1 kg mass by 1 m/s².
