Concept Of Physics Introduction to Physics

H C Verma

Concept Of Physics

1.   Find the dimensions of

A. linear momentum,

B. frequency and

C. pressure.

A. $ mv = [ MLT^{-1} ] $

B. Frequency $ \dfrac{1}{t} = [ M^0L^0T^{-1} ] $

C. $ \dfrac{Force}{Area} = \dfrac{[MLT^{-2}]}{L^2} = [ML^{-1}T^{-2}] $

2.   Find the dimensions of

A. angular speed $\omega$

B. angular acceleration $\alpha$

C. torque $\Gamma$ and

D. moment of interia $I$

Some of the equations involving these quantities are

$ \omega = \dfrac{\theta_2 - \theta_1}{t_2 - t_1} , \alpha = \dfrac{\omega_2 - \omega_1}{t_2 - t_1} , \Gamma = F.r $ and $ I = mr^2 $ The symbols have standard meanings.

A. angular speed $\omega = \dfrac{\theta}{t} = [ M^0 L^0 T^{-1} ]$

B. angular acceleration $\alpha = \dfrac{\omega}{t} = \dfrac{M^0 L^0 T^{-2}}{T} = [M^0L^0T^{-3}]$

C. torque $\Gamma = F r = [MLT^{-2}][L] = [ML^2T^{-2}]$

D. moment of interia $I = Mr^2 = [M][L^2] = [ML^2T^0]$

3.   Find the dimensions of

A. electric field $ E $,

B. magnetic field $ B $ and

C. magnetic permeability $ \mu_0 $

The relevant equations are
$ F = qE, F = qvB $, and $ B = \dfrac{\mu_0 I}{2\pi \alpha} $

where $F$ is force, $q$ is charge,$ v$ is speed, $I$ is current, and $ a $ is distance.

A. Electric field $E = \dfrac{F}{q} = \dfrac {MLT^{-2}}{[IT]} = [MLT^{-3}{-1}] $

B. Magnetic field $B = \dfrac{F}{qv} = \dfrac{MLT^{-2}}{[IT][LT^{-1}]} = [MT^{-2} I^{-1} ] $

C. Magnetic permeability $ \mu_0 = \dfrac {B 2\pi a}{I} = \dfrac {MT^{-2} I^{-1} [L] }{[I]} = [MLT^{-2} I^{-2} ] $

4.   Find the dimensions of

A. electric dipole moment $p$ and

B. electric dipole moment $M$

The defining equations are $p = q.d$ and $M = IA$; where $d$ is distance, $A$ is area, $q$ is charge and $I$ is current.

A. Electric dipole moment $P = qI = [IT] × [L] = [LTI]$

B. Magnetic dipole moment $ M = IA = [I] [L^{2}] [L^{2}I]$

5.   Find the dimensions of Planck's constant $h$ from the equation $E = hv$ where $E$ is the energy and $v$ is the frequency.

$E = hv$ where $E =$ energy and $v=$ frequency
$ h = \dfrac{E}{v} = \dfrac{[ML^2T^{-2}] }{T^{-1}} = [ML^2 T^{-1}] $

6.   Find the dimensions of

A. the specific heat capacity $c $,

B. the coefficient of linear expansion a $ \alpha $ and

C. the gas constant $R$.

Some of the equations involving these quantities are

$Q = mc(T_2 - T_1), l_t=l_0[1+ a(T_2 - T_3)] $ and $ PV = nRT.$

A. Specific heat capacity $= C = \dfrac{Q}{m \Delta T} = \dfrac{[ML^2T^{-2}]}{[M][K]} = [L^2T^{-2} K^{-1}] $

B. Coefficient of linear expansion = $ \alpha = \dfrac{L_1 - L_2}{L_0 \Delta T} = \dfrac{[L]}{[L][R]} = [K^{-1}] $

C. Gas constant $= R = \dfrac{PV}{nT} = \dfrac{[ML^{-2} T^{-2} ][L^3]}{[(mol)][K]} = [ML^2T^{-2}K^{-1} (mol)^{-1} ] $

7.   Taking force, length and time to be the fundamental quantities find the dimensions of

A. density,

B. pressure,

C. momentum and

D. energy.

Taking force, length and time as fundamental quantity

A. Density $= \dfrac{m}{V} = \dfrac{(force/acceleration)}{Volume} = \dfrac{[F/LT^{-2}]}{[L^2]} = \dfrac{F}{L^4T^{-2}} = [FL^{-4} T^2]$

B. Pressure $= \dfrac{F}{A} = \dfrac{ F}{L^2}= [FL^{-2}]$

C. Momentum $= mv (Force / acceleration) × Velocity = [F / LT^{-2}] × [LT^{-1}] = [FT]$

D. Energy $ = \dfrac {1}{2}{mv^2} = \dfrac {Force}{acceleration} {(velocity)^2} $

$ \dfrac {F}{LT^{-2}} [LT^{-1}]^2 = \dfrac {F}{LT^{-2}} [L^2T^{-2}] = [FL] $

8.   Suppose the acceleration due to gravity at a place is 10 $m/s^2$ . Find its value in $cm/(minute)^2$

$ g=10 \dfrac{meter}{sec^2} = 36 \times 10^5 cm/min^2$