Question 55: Units , Dimensions and Error Analysis

Question

Match List - I with List - II.

List - I
List - II

(A) Young’s Modulus
(I) M L-1 T-1

(B) Torque
(II) M L-1 T-2

(C) Coefficient of Viscosity
(III) M-1 L3 T-2

(D) Gravitational Constant
(IV) M L2 T-2

Choose the correct answer from the options given below :

Accepted Answer

We know, Young's modulus, $$E = {\sigma  \over \varepsilon }$$
$$ \Rightarrow E = {{{F \over A}} \over {{{\Delta L} \over L}}} = {F \over A}\left( {{L \over {\Delta L}}} ight)$$
$$ \Rightarrow [E] = {{[F]} \over {[A]}} = {{\left[ {{M^1}{L^1}{T^{ - 2}}} ight]} \over {\left[ {{L^2}} ight]}}$$
(A) $$ \Rightarrow [E] = [{M^1}{L^{ - 1}}{T^{ - 2}}]$$
(B) we know, Torque = $r	imes F$
$$[	au ] = [r][F]$$
$$ = [L][{M^1}{L^1}{T^{ - 2}}]$$
$$[	au ] = [{M^1}{L^2}{T^{ - 2}}]$$
(C) We know, $$F = \mu A{u \over y}$$
where, F = force, $\mu$ = coefficient of viscosity
A = area $\frac{u}{y}$ = rate of shear deformation
$$ \Rightarrow \mu  = {{Fy} \over {Au}}$$
$$ \Rightarrow [\mu ] = {{[{M^1}{L^1}{T^{ - 2}}][L]} \over {[{L^2}][L{T^{ - 1}}]}}$$
$$ \Rightarrow [\mu ] = [{M^1}{L^{ - 1}}{T^{ - 1}}]$$
(D) We know, $$F = {{G{m_1}{m_2}} \over {{r^2}}}$$ (Newton's law of gravitation)
$$ \Rightarrow G = {{F{r^2}} \over {{m_1}{m_2}}}$$<$$ \Rightarrow G = {{F{r^2}} \over {{m_1}{m_2}}}$$
$$ \Rightarrow [G] = {{[{M^1}{L^1}{T^{ - 2}}][{L^2}]} \over {[{M^2}]}}$$
$$ \Rightarrow [G] = [{M^{ - 1}}{L^3}{T^{ - 2}}]$$
Hence, option D is correct.

Answer

(A)-(I), (B)-(III), (C)-(II), (D)-(IV)

Answer

(A)-(IV), (B)-(II), (C)-(III), (D)-(I)

Answer

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Answer

(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

Units , Dimensions and Error Analysis

Match List - I with List - II. List - I List - II (A) Young’s Modulus (I) M L-1 T-1 (B) Torque (II) M L-1 T-2 (C) Coefficient of Viscosity (III) M-1 L3 T-2 (D) Gravitational Constant (IV) M L2 T-2 Choose the correct answer from the options given below :

Choose the correct answer: