NEET Units and Measurements Previous year Question

4.(NEET 2024 )

The quantities which have the same directions as those of solid angle are:

A.strain and angle

B.stress and angle

C.strain and arc

D.angular speed and stress

Correct option is (A)

Solid angle $d Ω = \frac{d A}{r^{2}}$ has dimensions $[M^{0} L^{0} T^{0}]$

Strain $= \frac{Δ l}{l}$ has dimensions $[M^{0} L^{0} T^{0}]$

Angle measured in radians is also dimensionless $[M^{0} L^{0} T^{0}]$

$θ = \frac{I}{r}$

5. (NEET 2023 Manipur )

The mechanical quantity, which has dimensions of reciprocal of mass $(M^{- 1})$ is :

(A) angular momentum

(B) coefficient of thermal conductivity

(C) torque

(D) gravitational constant

Correct answer is (D)

Angular momentum $= [{ML}^{2} T^{- 1}]$

Coeff of thermal conductivity $= [{MLT}^{- 3} K^{- 1}]$

Torque $= [{ML}^{2} T^{- 2}]$

Gravitational constant $= [M^{- 1} L^{3} T^{- 2}]$

So, gravitational constant has power of $(- 1)$ of $M$ .

6. (NEET 2022 Phase 2 )

The physical quantity that has the same dimensional formula as pressure is

(A) Coefficient of viscosity

(B) Force

(C) Momentum

(D) Young's modulus of elasticity

Correct answer is (D)

Pressure $[P] = [\frac{F}{A}] = [\frac{M L T^{- 2}}{L^{2}}] = [M L^{- 1} T^{- 2}]$

And, dimensions of Young's modulus $[Y] = [\frac{S t r e s s}{S t r a i n}] = [M L^{- 1} T^{- 2}]$

[Force] $= [M L T^{- 2}]$

[Momentum] $= [M L T^{- 1}]$

[Coefficient of viscosity] $= [M L^{- 1} T^{- 1}]$

7. (NEET 2022 Phase 1 )

The dimensions [MLT^{$-$ 2}A^{$-$ 2}] belong to the

(A) Magnetic flux

(B) Self inductance

(C) Magnetic permeability

(D) Electric permittivity

Correct answer is (C)

Dimensional formula of magnetic permeability is [MLT^{$-$ 2}A^{$-$ 2}]

8. (NEET 2022 Phase 1 )

Plane angle and solid angle have

(A) Units but no dimensions

(B) Dimensions but no units

(C) No units and no dimensions

(D) Both units and dimensions

Correct answer is (C)

Plane angle = $\frac{A r c}{R a d i u s} = \frac{[L]}{[L]} \overset{}{⟶}$ Unit = Radian

= [M^{0} L^{0} T^{0}]

Solid angle = $\frac{A r e a}{{(R a d i u s)}^{2}} \overset{}{⟶}$ Unit = Steradian

$= \frac{L^{2}}{L^{2}} = [M^{0} L^{0} T^{0}]$

$∴$ Both have units but no dimensions.