NEET Units and Measurements Previous year Question

9. (NEET 2021 )

The E and G respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of :

(A) [M²] [L^{$-$ 2}] [T^{$-$ 1}]

(B) [M²] [L^{$-$ 1}] [T⁰]

(C) [M] [L^{$-$ 1}] [T^{$-$ 1}]

(D) [M] [L⁰] [T⁰]

Correct answer is (B)

E = energy = [ML²T^{$-$ 2}]

G = Gravitational constant = [M^{$-$ 1}L³T^{$-$ 2}]

So, $\frac{E}{G} = \frac{[E]}{[G]} = \frac{M L^{2} T^{- 2}}{M^{- 1} L^{3} T^{- 2}} = [M^{2} L^{- 1} T^{0}]$

10. (NEET 2020 Phase 1 )

Dimensions of stress are :

(A) $[M L^{2} T^{- 2}]$

(B) $[M L^{0} T^{- 2}]$

(C) $[M L^{- 1} T^{- 2}]$

(D) $[M L^{} T^{- 2}]$

Correct answer is (C)

$S t r e s s = \frac{F o r c e}{A r e a}$

$= [\frac{M L T^{- 2}}{L^{2}}] = [M L^{- 1} T^{- 2}]$

11. (NEET 2013 (Karnataka) )

The pair of quantities having same dimensions is

(A) Impulse and Surface Tension

(B) Angular momentum and Work

(C) Work and Torque

(D) Young's modulus and Energy

Correct answer is (C)

Work = Force $\times$ distance = [MLT^-2][L] = [ML²T^-2]

Torque = Force $\times$ Force arm = [MLT^-2][L] = [ML²T^-2]

12. (AIPMT 2012 Mains )

The dimensions of ${(μ_{0} ε_{0})}^{- 1 / 2}$ are

(A) $[L^{1 / 2} T^{- 1 / 2}]$

(B) $[L^{- 1} T]$

(C) $[L T^{- 1}]$

(D) $[L^{1 / 2} T^{1 / 2}]$

Correct answer is (C)

${(μ_{0} ε_{0})}^{- 1 / 2}$ = $\frac{1}{\sqrt{μ_{0} ε_{0}}}$ = Speed of light in vacuum = c

So the dimension of ${(μ_{0} ε_{0})}^{- 1 / 2}$ = [c] =[LT^-1]

13. (AIPMT 2011 Prelims )

The dimensions of ${(μ_{0} ε_{0})}^{- 1 / 2}$ are

(A) $[L^{1 / 2} T^{- 1 / 2}]$

(B) $[L^{- 1} T]$

(C) $[L T^{- 1}]$

(D) $[L^{1 / 2} T^{1 / 2}]$

Correct answer is (C)

${(μ_{0} ε_{0})}^{- 1 / 2}$ = $\frac{1}{\sqrt{μ_{0} ε_{0}}}$ = Speed of light in vacuum = c

So the dimension of ${(μ_{0} ε_{0})}^{- 1 / 2}$ = [c] =[LT^-1]