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Q. No.The expression for time, in terms of the universal gravitational constant \(G,\) Planck’s constant \(h,\) and the speed of light \(c,\) is proportional to:
1.
\(\sqrt{\dfrac{hc^5}{G}}\)
2.
\(\sqrt{\dfrac{c^3}{Gh}}\)
3.
\(\sqrt{\dfrac{Gh}{c^5}}\)
4.
\(\sqrt{\dfrac{Gh}{c^3}}\)
Subtopic: Dimensions |
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Level 2: 60%+
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The percentage errors in quantities \(P, Q, R\) and \(S\) are \(0.5\%,\) \(1\%,\) \(3\%\) and \(1.5\%\) respectively in the measurement of a physical quantity \(A = \frac{P^3Q^2}{\sqrt {R}S}.\) The maximum percentage error in the value of \(A\) will be:
1. \(6.5\%\)
2. \(7.5\%\)
3. \(6.0\%\)
4. \(8.5\%\)
1. \(6.5\%\)
2. \(7.5\%\)
3. \(6.0\%\)
4. \(8.5\%\)
Subtopic: Errors |
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Level 1: 80%+
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A physical quantity \(P\) is described by the relation \({P}={a}^\frac{1}{2}{b}^2{c}^3{d}^{-4}.\) If the relative errors in the measurement of \({a, b, c}\) and \({d}\) respectively are \(2\%,1\%,3\%\) and \(5\%,\) then the relative error in \(P\) will be:
1. \(25\%\)
2. \(12\%\)
3. \(8\%\)
4. \(32\%\)
1. \(25\%\)
2. \(12\%\)
3. \(8\%\)
4. \(32\%\)
Subtopic: Errors |
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The relative error in the determination of the surface area of a sphere is \(\alpha.\) Then the relative error in the determination of its volume is:
1. \(\dfrac{3}{2}\alpha\)
2. \(\dfrac{2}{3}\alpha\)
3. \(\alpha\)
4. \(\dfrac{5}{2}\alpha\)
1. \(\dfrac{3}{2}\alpha\)
2. \(\dfrac{2}{3}\alpha\)
3. \(\alpha\)
4. \(\dfrac{5}{2}\alpha\)
Subtopic: Errors |
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In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25 ~\text{cm}.\) There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main scale divisions and \(30\) circular scale divisions. Assuming negligible zero error, the thickness of the wire is:
1. \(0.4300~\text{cm}\)
2. \(0.3150~\text{cm}\)
3. \(0.0430~\text{cm}\)
4. \(0.2150~\text{cm}\)
1. \(0.4300~\text{cm}\)
2. \(0.3150~\text{cm}\)
3. \(0.0430~\text{cm}\)
4. \(0.2150~\text{cm}\)
Subtopic: Measurement & Measuring Devices |
Level 3: 35%-60%
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A copper wire is stretched to make it \(0.5\%\) longer. The percentage change in its electric resistance, if its volume remains unchanged, is:
1. \(2.0 \%\)
2. \(2.5 \%\)
3. \(1.0 \%\)
4. \(0.5 \%\)
1. \(2.0 \%\)
2. \(2.5 \%\)
3. \(1.0 \%\)
4. \(0.5 \%\)
Subtopic: Errors |
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Time \({(T)},\) velocity \({(C)}\) and angular momentum \({(h)}\) are chosen as fundamental quantities instead of mass, length, and time. In terms of these, the dimensions of mass would be:
1. \([{M}]=[{T}^{-1}{C}^2 {h}] \)
2. \([{M}]=[{T}^{-1}{C}^{-2} {h}^{-1}]\)
3. \([{M}]=[{T}^{-1} {C}^{-2} {h}]\)
4. \([{M}]=[{T} ~{C}^{-2} {h}]\)
1. \([{M}]=[{T}^{-1}{C}^2 {h}] \)
2. \([{M}]=[{T}^{-1}{C}^{-2} {h}^{-1}]\)
3. \([{M}]=[{T}^{-1} {C}^{-2} {h}]\)
4. \([{M}]=[{T} ~{C}^{-2} {h}]\)
Subtopic: Dimensions |
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A beaker contains a fluid of density \({p}~\text{kg/m}^{3},\) specific heat \({S}~\text{J/kg}^\circ \text{C}\) and viscosity \(\eta.\) The beaker is filled up to height \(h.\) To estimate the rate of heat transfer per unit area \({Q/A}\) by convection when the beaker is put on a hot plate, a student proposes that it should depend on \(\eta.\) \(\left(\frac{{S} \Delta \theta}{{h}}\right),\) and \(\left ({1\over pg} \right)\) when \(\Delta \theta\) (in \(\mathrm{^\circ C}\)) is the difference in the temperature between the bottom and top of the fluid. In that situation, the correct option for \({(Q/A})\) is:
1. \({\eta\left(\frac{S \Delta \theta}{h}\right)\left(\frac{1}{\rho g}\right)}\)
2. \({\eta\left(\frac{S \Delta \theta}{\eta h}\right)\left(\frac{1}{\rho g}\right)}\)
3. \({S\Delta \theta\over \eta h}\)
4. \(\eta{S\Delta \theta\over h}\)
1. \({\eta\left(\frac{S \Delta \theta}{h}\right)\left(\frac{1}{\rho g}\right)}\)
2. \({\eta\left(\frac{S \Delta \theta}{\eta h}\right)\left(\frac{1}{\rho g}\right)}\)
3. \({S\Delta \theta\over \eta h}\)
4. \(\eta{S\Delta \theta\over h}\)
Subtopic: Dimensions |
Level 3: 35%-60%
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The diameter of a steel ball is measured using vernier calipers which have divisions of \(0.1~\text{cm}\) on its main scale (MS) and \(10\) divisions of its vernier scale (VS) match \(9\) divisions on the main scale. Three such measurements for a ball are given as:
If the zero error is \(– 0.03~\text{cm},\) then the mean corrected diameter is :
1. \(0.53~\text{cm}\)
2. \(0.56~\text{cm}\)
3. \(0.59~\text{cm}\)
4. \(0.52~\text{cm}\)
| S.No | MS \(\text{(cm)}\) | VS divisions |
| 1 | 0.5 | 8 |
| 2 | 0.5 | 4 |
| 3 | 0.5 | 6 |
1. \(0.53~\text{cm}\)
2. \(0.56~\text{cm}\)
3. \(0.59~\text{cm}\)
4. \(0.52~\text{cm}\)
Subtopic: Errors |
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If the capacitance of a nanocapacitor is measured in terms of a unit \({‘u’}\) made by combining the electronic charge \({‘e’},\) the Bohr radius \('{a}_0 ’,\) and the Planck's constant \({‘h’}\) and speed of light \({‘c’}\) then:
1. \(u=\frac{e^2 h}{e a_0}\)
2. \(u=\frac{{e}^2 {c}}{h {a}_0}\)
3. \(u=\frac{h c}{e^2 a_0}\)
4. \(u=\frac{e^2a_0}{hc}\)
1. \(u=\frac{e^2 h}{e a_0}\)
2. \(u=\frac{{e}^2 {c}}{h {a}_0}\)
3. \(u=\frac{h c}{e^2 a_0}\)
4. \(u=\frac{e^2a_0}{hc}\)
Subtopic: Dimensions |
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Level 3: 35%-60%
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