Taking force, length and time to be fundamental quantities find the dimensions of
(a)Density,
(b)Pressure,
(c) momentum and
(d)energy
(a) Density $=\frac{\text { mass }}{\text { volume }}=\frac{\frac{\text { force }}{\text { accelearation }}}{\text { volume }}=\left[\mathrm{F} / \mathrm{LT}^{-2}\right]\left[\mathrm{L}^{3}\right]=\left[\mathrm{FL}-4 \mathrm{~T}^{-2}\right]$
(b) Pressure $=$ force/area $=[F] \backslash\left[L^{2}\right]=\left[\mathrm{FL}^{-2}\right]$
(c) Momentum $=\frac{\text { force }}{\text { acceleration }} \times$ velocity $=[\mathrm{F}] /\left[\mathrm{LT}^{-2}\right] \times\left[\mathrm{LT}^{-1}\right]=[\mathrm{FT}]$
(d) Energy $==\overline{\text { acceleration }} \times(\text { velocity })^{2}=[\mathrm{F}] /[\mathrm{LT}-2] \times\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right]=[\mathrm{FL}]$
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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,