Find the best tutors and institutes for Class 11 Tuition
Q4.16:
Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
Solution :
Step 1: Given Variables & System Parameters
We are given two masses connected by a light inextensible string passing over a massless, frictionless pulley. The parameters are defined as follows:
- Mass $m_1 = 8\text{ kg}$
- Mass $m_2 = 12\text{ kg}$
- Acceleration due to gravity $g \approx 9.8\text{ m/s}^2$
- String: Light and inextensible (Tension $T$ is uniform throughout the string)
- Pulley: Frictionless and massless
Step 2: Free Body Diagram (FBD) and Equations of Motion
Since $m_2 > m_1$, the system will accelerate with $m_2$ moving downward with acceleration $a$ and $m_1$ moving upward with the same acceleration $a$ [Per Newton’s Second Law].
For mass $m_1$ (upward motion):
$T - m_1g = m_1a$ --- (Equation 1)For mass $m_2$ (downward motion):
$m_2g - T = m_2a$ --- (Equation 2)Step 3: Calculating Acceleration ($a$)
Adding Equation 1 and Equation 2 to eliminate $T$:
$(T - m_1g) + (m_2g - T) = m_1a + m_2a$ $(m_2 - m_1)g = (m_1 + m_2)a$ $a = \left( \frac{m_2 - m_1}{m_1 + m_2} \right)g$Substituting the values:
$a = \left( \frac{12 - 8}{12 + 8} \right) \times 9.8$ $a = \left( \frac{4}{20} \right) \times 9.8 = 0.2 \times 9.8$ $a = 1.96\text{ m/s}^2$Step 4: Calculating Tension ($T$)
Substitute $a$ into Equation 1:
$T = m_1(g + a)$ $T = 8 \times (9.8 + 1.96)$ $T = 8 \times 11.76$ $T = 94.08\text{ N}$Step 5: Tabular Summary of Results
| Parameter | Result |
|---|---|
| Acceleration ($a$) | $1.96\text{ m/s}^2$ |
| Tension ($T$) | $94.08\text{ N}$ |
Final Solution: The acceleration of the masses is $1.96\text{ m/s}^2$ and the tension in the string is $94.08\text{ N}$.
More Questions from Class 11 Physics Laws of Motion EXERCISES
- Q4.1(a): Give the magnitude and direction of the net force acting on a drop of rain falling down with a constant speed,
- Q4.1(b): Give the magnitude and direction of the net force acting on a cork of mass 10 g floating on water,
- Q4.1(c): Give the magnitude and direction of the net force acting on a kite skillfully held stationary in the sky,
- Q4.1(d): Give the magnitude and direction of the net force acting on a car moving with a constant velocity of 30 km/h on a rough road,
- Q4.1(e): Give the magnitude and direction of the net force acting on a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
- Q4.10: A body of mass 0.40 kg moving initially with a constant speed of 10 (m s^{-1}) to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be (t = 0), the position of the body at that time to be (x = 0), and predict its position at (t = -5) s, 25 s, 100 s.
- Q4.11(a): A truck starts from rest and accelerates uniformly at 2.0 (m s^{-2}). At (t = 10) s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the velocity of the stone at (t = 11)s ? (Neglect air resistance.)
- Q4.11(b): A truck starts from rest and accelerates uniformly at 2.0 (m s^{-2}). At (t = 10) s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the acceleration of the stone at (t = 11)s ? (Neglect air resistance.)
- Q4.12(a): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 (m s^{-1}). What is the trajectory of the bob if the string is cut when the bob is at one of its extreme positions,
- Q4.12(b): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 (m s^{-1}). What is the trajectory of the bob if the string is cut when the bob is at its mean position.
- Q4.13(a): A man of mass 70 kg stands on a weighing scale in a lift which is moving upwards with a uniform speed of 10 (m s^{-1}). What would be the readings on the scale in this case?
- Q4.13(b): A man of mass 70 kg stands on a weighing scale in a lift which is moving downwards with a uniform acceleration of 5 (m s^{-2}). What would be the readings on the scale in this case?
- Q4.13(c): A man of mass 70 kg stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 (m s^{-2}). What would be the readings on the scale in this case?
- Q4.13(d): A man of mass 70 kg stands on a weighing scale in a lift. What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?
- Q4.14(a): Figure 4.16 shows the position-time graph of a particle of mass 4 kg. What is the force on the particle for (t < 0), (t > 4) s, (0 < t < 4) s? (Consider one-dimensional motion only).
- Q4.14(b): Figure 4.16 shows the position-time graph of a particle of mass 4 kg. What is the impulse at (t = 0) and (t = 4) s ? (Consider one-dimensional motion only).
- Q4.15(i): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force (F = 600) N is applied to the 10 kg body (A) along the direction of string. What is the tension in the string?
- Q4.15(ii): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force (F = 600) N is applied to the 20 kg body (B) along the direction of string. What is the tension in the string?
- Q4.17: A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
- Q4.18: Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 (m s^{-1}) collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
- Q4.19: A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 (m s^{-1}), what is the recoil speed of the gun ?
- Q4.2(a): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, during its upward motion,
- Q4.2(b): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, during its downward motion,
- Q4.2(c): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45(^{\circ}) with the horizontal direction? Ignore air resistance.
- Q4.20: A batsman deflects a ball by an angle of 45(^{\circ}) without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)
- Q4.21: A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
- Q4.22: If the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks :
- Q4.23(a): Explain why a horse cannot pull a cart and run in empty space,
- Q4.23(b): Explain why passengers are thrown forward from their seats when a speeding bus stops suddenly,
- Q4.23(c): Explain why it is easier to pull a lawn mower than to push it,
- Q4.23(d): Explain why a cricketer moves his hands backwards while holding a catch.
- Q4.3(a): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, just after it is dropped from the window of a stationary train,
- Q4.3(b): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, just after it is dropped from the window of a train running at a constant velocity of 36 km/h,
- Q4.3(c): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, just after it is dropped from the window of a train accelerating with 1 (m s^{-2}),
- Q4.3(d): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, lying on the floor of a train which is accelerating with 1 (m s^{-2}), the stone being at rest relative to the train. Neglect air resistance throughout.
- Q4.4: One end of a string of length (l) is connected to a particle of mass (m) and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed (v) the net force on the particle (directed towards the centre) is : (T) is the tension in the string.
- Q4.5: A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 (m s^{-1}). How long does the body take to stop ?
- Q4.6: A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 (m s^{-1}) to 3.5 (m s^{-1}) in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?
- Q4.7: A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
- Q4.8: The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.
- Q4.9: A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 (m s^{-2}). Calculate the initial thrust (force) of the blast.
- Q5.1(a): Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed,
- Q5.1(b): Give the magnitude and direction of the net force acting on (b) a cork of mass 10 g floating on water,
- Q5.1(c): Give the magnitude and direction of the net force acting on (c) a kite skillfully held stationary in the sky,
- Q5.1(d): Give the magnitude and direction of the net force acting on (d) a car moving with a constant velocity of 30 km/h on a rough road,
- Q5.1(e): Give the magnitude and direction of the net force acting on (e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
- Q5.10: A body of mass 0.40 kg moving initially with a constant speed of $10 m s^{-1}$ to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be $t = 0$, the position of the body at that time to be $x = 0$, and predict its position at $t = –5 s$, $25 s$, $100 s$.
- Q5.11(a): A truck starts from rest and accelerates uniformly at $2.0 m s^{-2}$. At $t = 10 s$, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity of the stone at $t = 11s$ ? (Neglect air resistance.)
- Q5.11(b): A truck starts from rest and accelerates uniformly at $2.0 m s^{-2}$. At $t = 10 s$, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (b) acceleration of the stone at $t = 11s$ ? (Neglect air resistance.)
- Q5.12(a): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is $1 m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions,
- Q5.12(b): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is $1 m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is (b) at its mean position.
- Q5.13(a): A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of $10 m s^{-1}$,
- Q5.13(b): A man of mass 70 kg stands on a weighing scale in a lift which is moving (b) downwards with a uniform acceleration of $5 m s^{-2}$,
- Q5.13(c): A man of mass 70 kg stands on a weighing scale in a lift which is moving (c) upwards with a uniform acceleration of $5 m s^{-2}$. What would be the readings on the scale in each case?
- Q5.13(d): A man of mass 70 kg stands on a weighing scale in a lift which is moving (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?
- Q5.14(a): Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for $t < 0$, $t > 4 s$, $0 < t < 4 s$?
- Q5.14(b): Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (b) impulse at $t = 0$ and $t = 4 s$ ? (Consider one-dimensional motion only).
- Q5.15(i): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force $F = 600 N$ is applied to (i) A, along the direction of string. What is the tension in the string in each case?
- Q5.15(ii): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force $F = 600 N$ is applied to (ii) B along the direction of string. What is the tension in the string in each case?
- Q5.16: Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
- Q5.17: A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
- Q5.18: Two billiard balls each of mass 0.05 kg moving in opposite directions with speed $6 m s^{-1}$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
- Q5.19: A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is $80 m s^{-1}$, what is the recoil speed of the gun ?
- Q5.2(a): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (a) during its upward motion,
- Q5.2(b): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (b) during its downward motion,
- Q5.2(c): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (c) at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45° with the horizontal direction? Ignore air resistance.
- Q5.20: A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)
- Q5.21: A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
- Q5.22: If, A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks :
- Q5.23(a): Explain why (a) a horse cannot pull a cart and run in empty space,
- Q5.23(b): Explain why (b) passengers are thrown forward from their seats when a speeding bus stops suddenly,
- Q5.23(c): Explain why (c) it is easier to pull a lawn mower than to push it,
- Q5.23(d): Explain why (d) a cricketer moves his hands backwards while holding a catch.
- Q5.3(a): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train,
- Q5.3(b): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,
- Q5.3(c): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (c) just after it is dropped from the window of a train accelerating with $1 m s^{-2}$,
- Q5.3(d): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (d) lying on the floor of a train which is accelerating with $1 m s^{-2}$, the stone being at rest relative to the train. Neglect air resistance throughout.
- Q5.4: One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : $T$ is the tension in the string. [Choose the correct alternative].
- Q5.5: A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of $15 m s^{-1}$. How long does the body take to stop ?
- Q5.6: A constant force acting on a body of mass 3.0 kg changes its speed from $2.0 m s^{-1}$ to $3.5 m s^{-1}$ in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?
- Q5.7: A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
- Q5.8: The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.
- Q5.9: A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of $5.0 m s^{-2}$. Calculate the initial thrust (force) of the blast.
CBSE Solutions for Class 11 Physics Laws of Motion
Chapters in CBSE - Class 11 Physics
Top Tutors who teach Laws of Motion
Super Tutor
H C Sarani, Kolkata
8 yrs of
Exp
18 students
1022 hrs of classes completed
500
per hour
Online Classes
I am a Chemistry tutor with over 11 years of teaching experience, specializing in Class 11 and 12 Chemistry, along with preparation for competitive exams like NEET and IIT JEE. Over the years, I have worked closely with students to help them build strong conceptual clarity, improve problem-solving skills, and achieve excellent academic results. My aim has always been to make Chemistry not only understandable but also interesting and engaging for every student. I hold a Bachelor of Science (B.Sc.), Master of Science (M.Sc.), and a Doctor of Philosophy (Ph.D.) in Chemistry. In addition, I have qualified NET-JRF (National Eligibility Test – Junior Research Fellowship), which reflects my strong academic background and subject expertise. These qualifications enable me to teach Chemistry at both fundamental and advanced levels with confidence and depth. Since 2015, I have been actively teaching students preparing for NEET and IIT-JEE, along with those appearing for CBSE and ISC board examinations. During this time, I have guided numerous students to achieve outstanding results by focusing on concept clarity and consistent practice. I take pride in seeing my students excel and develop confidence in tackling even the most challenging problems. My teaching approach is structured and systematic. I follow a clear lesson plan for every topic, ensuring that concepts are covered step by step, starting from the basics and gradually progressing to advanced levels. This method helps students build a strong foundation and makes it easier for them to understand complex topics. I believe in making my classes highly interactive, where students feel comfortable asking questions and participating in discussions. I emphasize conceptual understanding rather than rote memorization, which allows students to apply their knowledge effectively in both board exams and competitive exams like NEET and IIT-JEE. To further enhance learning, I incorporate practical examples and problem-based learning wherever possible. Each session includes detailed explanations followed by practice questions to reinforce understanding. I also provide exam-oriented guidance, including shortcuts, problem-solving techniques, and time management strategies to help students perform confidently. I conduct online classes, making learning accessible and convenient for students. My goal is to continue helping students explore the fascinating world of Chemistry while equipping them with the right skills and strategies to succeed in their academic and competitive exam journeys.
Ms. Tuyan was able to clear all my doubts and she helped me understand the concepts very nicely. She made learning chemistry easy, and I was able to grasp various points not previously understood.
Super Tutor
Kasavanahalli Main Rd Kasavanahalli, Bangalore
2 yrs of
Exp
1 student
900 hrs of classes completed
800
per hour
Online Classes
I am a teacher. I love teaching and want to share my knowledge with my students. I will take online classes. My approach combines clear concepts, regular practice, and student-friendly strategies to make learning effective and enjoyable.
Top Tutor
Anna Nagar Mullai Nagar, Chennai
9 yrs of
Exp
6 students
420 hrs of classes completed
600
per hour
Online Classes
Hi, I'm Kalaiselvi, an M.Sc. Mathematics graduate with 9 years of experience in one-on-one online Maths tutoring. I specialize in teaching Classes 10, 11, and 12 for CBSE and Tamil Nadu State Board. My classes are conducted in both English and Tamil (bilingual), making concepts easy to understand. I focus on concept clarity, problem-solving, regular practice, and exam preparation, with personalized attention for every student.
Great experience with Kalaiselvi Ma'am, her knowledge and skill on the subject are amazing. Thank you for your support and guidance.
Top Tutor
Sector 39 Charmwood Village, Faridabad
6 yrs of
Exp
3 students
112 hrs of classes completed
500
per hour
Online Classes
In my experience providing tuition for Class 11 students, I aimed to create a supportive and engaging learning environment tailored to their unique needs. I focused on key subjects such as English, Social Studies which are crucial for their board examinations. Teaching Methodology: I began each session by assessing the students’ current understanding and identifying specific areas where they needed support. This allowed me to customize my lesson plans to address their weaknesses while reinforcing their strengths. I employed a variety of teaching methods, including: Interactive Discussions: I encouraged students to participate actively by asking questions and engaging in discussions around key concepts, which helped to deepen their understanding. Problem-Solving Sessions: In subjects like Mathematics and Science, I emphasized problem-solving techniques. I walked them through complex problems step-by-step, encouraging them to think critically and develop their reasoning skills. Practice Tests: I conducted regular quizzes and mock tests to familiarize them with the exam format and to track their progress. This also helped reduce anxiety leading up to their actual exams. Student Engagement: To keep students motivated, I incorporated real-life applications of the concepts we covered. For example, in Science, I would relate topics to everyday phenomena, making the material more relatable and interesting. I also encouraged peer collaboration, allowing students to work together on challenging problems, fostering teamwork and communication skills. Feedback and Support: I provided constructive feedback on their work, highlighting both areas of improvement and their successes. I made myself available for additional support outside of regular sessions, whether through email or online messaging, to answer questions and clarify doubts. Results and Impact: Many of my students showed significant improvement in their confidence and academic performance. Witnessing their growth, especially as they prepared for their board exams, was incredibly rewarding. I emphasized the importance of a positive mindset, helping them develop not just academically, but also personally. Overall, my experience teaching Class 11 tuition was fulfilling, as I was able to make a meaningful impact on my students' educational journeys while fostering a love for learning.
Satisfactory, command on subject. Very well described the topic it was just a demo class , rest depends on other topics, though I found mam is sweet n goo in her subject.
Top Tutor
Satellite, Ahmedabad
9 yrs of
Exp
2 students
117 hrs of classes completed
1000
per hour
Online Classes
Student's Home
Tutor's home
Hello sir, this message is regarding your enquiry in urbanpro for Chemistry and mathematics tutor. This is SUYOG BAKLIWAL. I have been training students for class CBSE, IB 11th ,12th, JEE and NEET for the last 7 years. About myself, I have done my B.Tech from DAIICT, Gandhinagar. I have been teaching to students from the past 7 years. I have worked in many reputed institutes like AAKASH and ALLEN.
