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#dimensional analysis

9 public questions tagged with this topic.

SI Units and Dimensional Formulae

If the unit of length is doubled, how is the unit of area affected?

Area is proportional to the square of length. So, if the unit of length doubles, the unit of area becomes four times larger. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Four times is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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SI Units and Dimensional Formulae

Which one of the following pairs has different dimensions?

Pressure and stress both share the same dimensional formula \[ML−1T−2\], but energy has \[ML2T−2\]. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Pressure and Energy is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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SI Units and Dimensional Formulae

Which of the following quantities has different dimensions?

Pressure has the dimensional formula \[ML−1T−2\] while the others represent forms of energy or work. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Pressure is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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SI Units and Dimensional Formulae

Which of the following is a dimensionless constant?

Refractive index is the ratio of two similar quantities (speed of light), making it dimensionless. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Refractive index is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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SI Units and Dimensional Formulae

Which of the following pairs have the same dimensions?

Torque and work both have the dimensional formula \[ML2T−2\]. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Work and Torque is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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SI Units and Dimensional Formulae

Which of the following is a derived unit in the SI system?

Derived units are obtained by combining base units. Examples include the Newton (N), Joule (J), and Pascal (Pa). As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Newton (N) is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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SI Units and Dimensional Formulae

In a new unit system, 1unit of mass\=0.25kg, 1unit of length\=0.1m, 1unit of time\=0.5s. What is 3J (1J\=1kg m2s−2) in t

\[J\]=\[M L2T−2\]. 3J=3kg×(1m)2×(1s)−2=3×(4×0.25)×(10×0.1)2×(2×0.5)−2=3×1×1×4=12new units. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that 12 new is correct because its dimensions and unit match the physical quantity asked.

Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae

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