Planck's constant (h),speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimensions of length?

(1) $\frac{\sqrt{hG}}{{c}^{3/2}}$

(2) $\frac{\sqrt{hG}}{{c}^{5/2}}$

(3) $\sqrt{\frac{hc}{G}}$

(4)$\sqrt{\frac{Gc}{{h}^{3/2}}}$

Subtopic:  Dimensions |
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If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

(1) $\left[\begin{array}{cc}E& {v}^{-2}{T}^{-1}\end{array}\right]$

(2) [$E{v}^{-1}{T}^{-2}$]

(3) $\left[\begin{array}{cc}E{v}^{-2}& {T}^{-2}\end{array}\right]$

(4) [${E}^{-2}{v}^{-{1}_{T}-3}$]

Subtopic:  Dimensions |
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In an experiment four quantities a, b, c and d are measured with percentage error 1%,2%,3% and 4% respectively. Quantity P is calculated as follows P=a3b2/cd %, Error in P is

1. 14%

2. 10%

3. 7%

4. 4%

Subtopic:  Errors |
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The density of material in the CGS system of units is $4g/c{m}^{3}.$ In a system of units in which unit of length is 10cm and unit of mass is 100g when the value of density of material in this system will be:

(1) 0.4

(2) 40

(3) 400

(4) 0.04

Subtopic:  Dimensions |
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A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are ${\mathrm{e}}_{1}$ and ${\mathrm{e}}_{2}$ respectively, the percentage error in the estimation of g is

1. ${\mathrm{e}}_{2}-{\mathrm{e}}_{1}$

2. ${\mathrm{e}}_{1}+2{\mathrm{e}}_{2}$

3. ${\mathrm{e}}_{1}+{\mathrm{e}}_{2}$

4. ${\mathrm{e}}_{1}-2{\mathrm{e}}_{2}$

Subtopic:  Errors |
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If the dimension of a physical quantity are given by ${\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}},$ then the physical quantity will be

(1) pressure if a=1, b=-1, c=-2

(2) velocity if a=1, b=0, c=-1

(3) acceleration if a=1, b=1,c=-2

(4) force if a=0, b=-1, c=-2

Subtopic:  Dimensions |
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If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:

1. 4%                                                   2. 6%

3. 8%                                                   4. 2%

Subtopic:  Errors |
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Which two of the following five physical parameters have the same dimensions ?

(1) energy density

(2) refractive index

(3) dielectric constant

(4) Young's modulus

(5) magnetic field

1. 2 and 4

2. 3 and 5

3. 1 and 4

4. 1 and 5

Subtopic:  Dimensions |
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A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{{e}^{2}}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}$is [c is the velocity of light, G is the universal constant of gravitation and e is charge]:

1. ${c}^{2}{\left[G\frac{{e}^{2}}{4\pi {\epsilon }_{0}}\right]}^{\frac{1}{2}}$

2. $\frac{1}{{c}^{2}}{\left[\frac{{e}^{2}}{4G\pi {\epsilon }_{0}}\right]}^{\frac{1}{2}}$

3. $\frac{1}{c}G\frac{{e}^{2}}{4\pi {\epsilon }_{0}}$

4. $\frac{1}{{c}^{2}}{\left[G\frac{{e}^{2}}{4\pi {\epsilon }_{0}}\right]}^{\frac{1}{2}}$

Subtopic:  Dimensions |
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A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is:

1. 0.521 cm

2. 0.525 cm

3. 0.053 cm

4. 0.529 cm

Subtopic:  Measurement & Measuring Devices |
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