If the acceleration due to gravity is 10 ms–2 and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is

(1) 360000

(2) 72,000

(3) 36,000

(4) 129600

Concept Questions :-

Dimensions
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Difficulty Level:

If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency                        [Only for droppers]

(1) $\frac{1}{RC}$

(2) $\frac{R}{L}$

(3) $\frac{1}{\sqrt{LC}}$

(4) $\frac{C}{L}$

Concept Questions :-

Dimensions
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Number of particles is given by $n=-D\frac{{n}_{2}-{n}_{1}}{{x}_{2}-{x}_{1}}$crossing a unit area perpendicular to X-axis in unit time, where n1 and n2 are number of particles per unit volume for the value of x meant to x2 and x1. Find dimensions of D called as diffusion constant

(1) ${M}^{0}L{T}^{2}$

(2) ${M}^{0}{L}^{2}{T}^{-4}$

(3) ${M}^{0}L{T}^{-3}$

(4) ${M}^{0}{L}^{2}{T}^{-1}$

Concept Questions :-

Dimensions
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Difficulty Level:

With the usual notations, the following equation ${S}_{t}=u+\frac{1}{2}a\left(2t-1\right)$ is

(1) Only numerically correct

(2) Only dimensionally correct

(3) Both numerically and dimensionally correct

(4) Neither numerically nor dimensionally correct

Concept Questions :-

Dimensions
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Difficulty Level:

If the dimensions of length are expressed as ${G}^{x}{c}^{y}{h}^{z}$; where G, c and h are the universal gravitational constant, speed of light and Planck's constant respectively, then

(1) $x=\frac{1}{2},\text{\hspace{0.17em}\hspace{0.17em}}y=\frac{1}{2}$

(2) $x=\frac{1}{2},\text{\hspace{0.17em}\hspace{0.17em}}z=\frac{1}{2}$

(3) $y=\frac{1}{2},\text{\hspace{0.17em}\hspace{0.17em}}z=\frac{3}{2}$

(4) $y=-\frac{3}{2},\text{\hspace{0.17em}\hspace{0.17em}}z=\frac{1}{2}$

Concept Questions :-

Dimensions
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Difficulty Level:

A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of low modulus of rigidity $\eta$ such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn block A executes small oscillations. The time period of which is given by

(1) $2\pi \sqrt{\frac{M\eta }{L}}$

(2) $2\pi \sqrt{\frac{L}{M\eta }}$

(3) $2\pi \sqrt{\frac{ML}{\eta }}$

(4) $2\pi \sqrt{\frac{M}{\eta L}}$

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Difficulty Level:

The pair(s) of physical quantities that have the do not have same dimensions, is (are)

(1) Reynolds number and coefficient of friction

(2) Latent heat and gravitational potential

(3) Curie and frequency of a light wave

(4) Planck's constant and torque

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Difficulty Level:

The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as the fundamental units in a system. The dimension of time in this new system should be

(1) ${G}^{1/2}{h}^{1/2}{c}^{-5/2}$

(2) ${G}^{-1/2}{h}^{1/2}{c}^{1/2}$

(3) ${G}^{1/2}{h}^{1/2}{c}^{-3/2}$

(4) ${G}^{1/2}{h}^{1/2}{c}^{1/2}$

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Difficulty Level:

If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimension of the radius of gyration is

(1) ${h}^{1/2}{c}^{-3/2}{G}^{1/2}$

(2) ${h}^{1/2}{c}^{3/2}{G}^{1/2}$

(3) ${h}^{1/2}{c}^{-3/2}{G}^{-1/2}$

(4) ${h}^{-1/2}{c}^{-3/2}{G}^{1/2}$

Concept Questions :-

Dimensions
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Difficulty Level:

X = 3YZ2 find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively

(1) ${M}^{-3}{L}^{-2}{T}^{-4}{A}^{-1}$

(2) ML–2

(3) ${M}^{-3}{L}^{-2}{T}^{4}{A}^{4}$

(4) ${M}^{-3}{L}^{-2}{T}^{8}{A}^{4}$

Concept Questions :-

Dimensions