Physical Quantities

Q.

Give examples of three physical quantities that are having dimensions [ $M{L}^{-1}{T}^{-2}$ ].

Q. If $\alpha \text{kilogram}$, $\beta \text{meter}$, and $\gamma \text{second}$ are the fundamental units, $1\text{cal}$ can be expressed in new units as $[1\text{cal}=4.2\text{J}]$

1. ${\alpha }^{-1}{\beta }^2\gamma$
2. ${\alpha }^{-1}{\beta }^{-2}\gamma$
3. $4.2{\alpha }^{-1}\beta$
4. $4.2{\alpha }^{-1}{\beta }^{-2}{\gamma }^2$

Q. What is the dimensional formula of angular momentum $L$ ?
$L=rp\sin \theta$, where $r$ is the position and $p$ is momentum.

1. $\text{[MLT}{}^{-1}\text{]}$
2. $\text{[M}{}^2\text{LT}{}^{-1}\text{]}$
3. $\text{[ML}{}^2\text{T}{}^{-1}\text{]}$
4. $\text{[M}{}^2\text{L}{}^2\text{T}{}^{-1}\text{]}$

Q. If the units of length and force are increased four times, then the unit of energy will

1. increase 8 times
2. increase 16 times
3. decrease 16 times
4. increase 4 times

Q. Which of the following options represents correct dimensions of ${ϵ}_o$?

1. $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
2. $\left[M^{-1}{L}^{-3}{T}^{3}A\right]$
3. $\left[M^{-1}{L}^{-3}T{A}^2\right]$
4. $\left[M^0{L}^{-3}{T}^3{A}^3\right]$

Q.

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are not present?

1. Easily available

2. Invariable

3. Indestructible

4. Easily reproducible

Q.

A force of 2500 N produces a pressure of 50, 000 Pa. Calculate the area of the surface on which the force acts.

Q. Dimensional formula $M{L}^{-1}{T}^{-2}$ does not represent the physical quantity

1. Young's modulus of elasticity
2. Stress
3. Strain
4. Pressure

Q. If force, time and velocity are treated as fundamental quantities, then dimensional formula of energy will be

1. $\left[FTV\right]$
2. $\left[F{T}^{2}V\right]$
3. $\left[FT{V}^2\right]$
4. $\left[F{T}^2{V}^2\right]$

Q. If velocity (v) of particle is given by v = at + bt², where t is time, then dimension of $\frac{a}{b}$ is

यदि कण के वेग (v) को v = at + bt² द्वारा व्यक्त किया जाता है, जहाँ t समय है, तब $\frac{a}{b}$ की विमा है

1. [M⁰L⁰T¹]
   
2. [M⁰L⁰T^–1]
   
3. [M⁰L⁰T^–2]
   
4. [M⁰L¹T⁰]
   

Q. Dimensional formula $M{L}^{-1}{T}^{-2}$ does not represent the physical quantity

1. Young's modulus of elasticity
2. Stress
3. Strain
4. Pressure