Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force
Question:
Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force $F$ at $a$ point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu=0.4$, the maximum possible value of $100 x$
$\frac{b}{a}$ for box not to topple before moving is_______
Solution:
(50) For the box to be slide
$F=\mu m g=0.4 \mathrm{mg}$
For no toppling
$F\left(\frac{a}{2}+b\right) \leq m g \frac{a}{2}$
$\Rightarrow 0.4 m g\left(\frac{a}{2}+b\right) \leq m g \frac{a}{2}$
$\Rightarrow 0.2 a+0.4 b \leq 0.5 a$
$\Rightarrow \frac{b}{a} \leq \frac{3}{4}$
i.e. $b \leq 0.75 a$ but this is not possible.
As the maximum value of $b$ can be equal to $0.5 a$.
$\Rightarrow \frac{100 b}{a}=50$
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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,
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