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

(a) $\frac{1}{{c}^{2}}{\left[G\frac{{e}^{2}}{4\pi {\epsilon }_{o}}\right]}^{1}{2}}$

(b) ${c}^{2}{\left[G\frac{{e}^{2}}{4\pi {\epsilon }_{o}}\right]}^{1}{2}}$

(c) $\frac{1}{{c}^{2}}{\left[\frac{{e}^{2}}{G4\pi {\epsilon }_{o}}\right]}^{1}{2}}$

(d) $\frac{1}{c}G\frac{{e}^{2}}{4\pi {\epsilon }_{0}}$

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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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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NEET 2023 - Target Batch - Aryan Raj Singh
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Planck's constant (h), speed of light in the vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

1.  $\frac{\sqrt{\mathrm{hG}}}{{\mathrm{c}}^{3/2}}$

2.  $\frac{\sqrt{\mathrm{hG}}}{{\mathrm{c}}^{5/2}}$

3.  $\frac{\sqrt{\mathrm{hG}}}{\mathrm{G}}$

4.  $\frac{\sqrt{\mathrm{Gc}}}{{\mathrm{h}}^{3/2}}$

Subtopic:  Dimensions |
To view explanation, please take trial in the course below.
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NEET 2023 - Target Batch - Aryan Raj Singh
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