Suppose the smaller pulley of the previous problem has its radius $5.0 \mathrm{~cm}$ and moment of inertia $0.1 \mathrm{kgm}^{2}$. Find the tension in the part of the string joining the pulleys.
$m g-T_{1}=m a-\cdots-(i)$
$\left(T_{1}-T_{2}\right) r_{1}=I_{1} \alpha-----(i i)$
$T_{2} r_{2}=I_{2} \alpha-\cdots--(i i i)$
substitutingthe value of $T_{2}$ in equation (ii)
$\left(T_{1}-\frac{I_{2} \alpha}{r_{2}}\right) r_{1}=I_{1} \alpha$
$T_{1}-\frac{I_{2} \alpha}{r_{2}}=\frac{I_{1} \alpha}{r_{1}}$
$a s$
$a=\alpha r$
$T_{1}-\frac{I_{2} a}{r_{2}^{2}}=\frac{I_{1} a}{r^{2}}$
$T_{1}=\left(\frac{I_{2}}{r_{2}^{2}}+\frac{I_{1}}{r_{1}^{2}}\right) a$
Substitutingthe value of $T_{1}$ in equation 1
we get
$m g-\left(\frac{I_{2}}{r_{2}^{2}}+\frac{I_{1}}{r_{1}^{2}}\right) a=m a$
Onsubstituting the values
$\mathrm{a}=0.316 \mathrm{~ms}^{-2}$
$T_{2}=6.32 \mathrm{~N}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,