A $6.5 \mathrm{~m}$ long ladder rests against a vertical wall reaching a height of $6.0 \mathrm{~m}$. A $60 \mathrm{~kg}$ man stands half way up the ladder. (a) Find the torque of the force exerted by the man on the ladder about the upper end of the ladder. (b)Assuming the weight of the ladder to be negligible as compared to the man and assuming the wall to be smooth, find the force exerted by the ground on the ladder.
By Pythagoras theorem,
$(6.5)^{2}=(6)^{2}+B^{2}$
$B=2.5 \mathrm{~m}$
(a) $\tau=F \times d_{\Perp}$
$\mathrm{T}=6 \lg _{6.5}\left(\frac{6.5}{2} \sin \theta\right.$
$=60 \mathrm{~g}\left(\frac{2.5}{6.5}\right)$
$=60 \mathrm{~g}\left(\frac{6.5}{2} \times \frac{2.5}{6.5}\right)$
$\tau=740 \mathrm{~N}-\mathrm{m}$
(b) $N_{1}=60 g$
(Vertical Translatory Equation)
Rotational Equilibrium at $O$
$N_{2}(6.5 \cos \theta)=60 g\left(\frac{6.5}{2} \sin \theta\right)$
$N_{2}=30 g \tan \theta$
$N_{2}=30 g\left(\frac{2.5}{6}\right)$
$N_{2}=120 \mathrm{~N}$
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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,