Free Body Diagram — Multi-body systems, pulleys
Laws of Motion
9
JEE Qs
8%
Hard
75
min
Systematically draw a clear FBD for each individual component, apply Newton's Second Law, and correctly establish all constraint relations to solve multi-body problems efficiently.
🧮 Key Formulas
✅ Key Points for JEE
- 1Isolate each body (mass, pulley if relevant) in the system and draw a separate Free Body Diagram (FBD) for it, showing *only* forces acting *on* that specific body.
- 2Identify all external forces acting on each isolated body, including weight (mg), normal force (N), tension (T), friction (if present), and any applied forces.
- 3Choose a consistent coordinate system for each body, typically aligning one axis with the direction of its acceleration to simplify force resolution and equation setup.
- 4Apply Newton's Second Law (ΣF = ma) along the chosen axes for each FBD, resulting in a system of simultaneous equations.
- 5Establish correct constraint relations for accelerations of connected bodies (e.g., inextensible strings, rigid connections, pulley motion) to solve the system of equations, as these reduce the number of independent variables.
⚠️ Common Mistakes
- ✕Incorrectly identifying forces (e.g., adding internal forces to an FBD or missing key external forces like normal force or tension).
- ✕Failing to draw separate FBDs for *each* component in the multi-body system, leading to confusion about which forces act on which body.
- ✕Incorrectly applying constraint relations for accelerations, especially in complex pulley systems where the pulley itself might be movable.
- ✕Assuming tensions in different string segments are equal without considering the pulley's mass or friction, or if multiple distinct strings are present.
- ✕Sign errors when resolving forces into components or when setting up equations of motion, often due to inconsistent choice of positive directions.
📝 Practice Questions
See allQ41.A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' 3a′ will be (Take ' g ' as acceleration due to gravity) (1) 2Ma (2) 3Ma 3a+g 2a−g (3) 3Ma (4) 2Ma 2a+g 3a−g
Q33.A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e. dmdt ∝√v . If P is the power delivered to run the belt at constant speed then which of the following relationship is true? 2025 (29 Jan Shift 2) JEE Main Previous Year Paper (1) P ∝√v (2) P ∝v (3) P2 ∝v5 (4) P2 ∝v3
Q29.A car of mass ' m ' moves on a banked road having radius ' r ' and banking angle θ. To avoid slipping from banked road, the maximum permissible speed of the car is v0 . The coefficient of friction μ between the wheels of the car and the banked road is θ θ tan tan 0−rg (1) μ = v2o+rg (2) μ = v2 θ tan θ rg−v2 tan rg+v2o 0 θ θ tan v2o+rg tan 0−rg (4) μ = (3) μ = v2 θ tan θ rg+v2 tan rg−v2o 0
Q47. A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes ( π3 ) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is … … ML.
Q5. A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curve best describes acceleration of the block with time: (1) (2) (3) (4)
Q21.Two forces ¯F1 and ¯F2 are acting on a body. One force has magnitude thrice that of the other force and the 1 ) resultant of the two forces is equal to the force of larger magnitude. The angle between →F1 and →F2 is cos−1 ( n . The value of |n| is _____.
NCERT Chapters
- Class 11 Physics Ch 5: Laws of Motion