Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure.
Suppose the disk makes $n$ number of revolutions to attain an angular speed of $50 \mathrm{rad} \mathrm{s}^{-1}$. The value of $\mathrm{n}$, to the nearest integer, is [Given : In one complete revolution, the disk rotates by $6.28 \mathrm{rad}$ ]
$\alpha=\frac{\tau}{\mathrm{I}}=\frac{\mathrm{F} \cdot \mathrm{R} .}{\mathrm{mR}^{2} / 2}=\frac{2 \mathrm{~F}}{\mathrm{mR}}$
$\alpha=\frac{2 \times 200}{20 \times(0.2)}=10 \mathrm{rad} / \mathrm{s}^{2}$
$\omega^{2}=\omega_{0}^{2}+2 \alpha \Delta \theta$
$(50)^{2}=0^{2}+2(10) \Delta \theta \Rightarrow \Delta \theta=\frac{2500}{20}$
$\Delta \theta=125 \mathrm{rad}$
No. of revolution $=\frac{125}{2 \pi} \approx 20$ revolution
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- 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,