A physical quantity \(P\) is related to four observations \(a,b,c\) and \(d\) as follows:
\(P=\dfrac{a^3b^2}{c\sqrt{d}}\)
The percentage errors of measurement in \(a,b,c\) and \(d\) are \(1\%,3\%,2\%\) and \(4\%\) respectively. The percentage error in the quantity \(P\) is:
\(P=\dfrac{a^3b^2}{c\sqrt{d}}\)
The percentage errors of measurement in \(a,b,c\) and \(d\) are \(1\%,3\%,2\%\) and \(4\%\) respectively. The percentage error in the quantity \(P\) is:
| 1. | \(13\%\) | 2. | \(15\%\) |
| 3. | \(10\%\) | 4. | \(2\%\) |
Subtopic: Errors |
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The sun rotates around its centre once in \(27\) days. What will be the period of revolution if the sun were to expand to twice its present radius without any external influence? Assume the sun to be a sphere of uniform density.
| 1. | \(115\) days | 2. | \(108\) days |
| 3. | \(100\) days | 4. | \(105\) days |
Subtopic: Angular Momentum |
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The radius of Martian orbit around the sun is about \(4\) times the radius of the orbit of mercury. The Martian year is \(687\) earth days. Then which of the following is the length of \(1\) year on mercury?
1. \(172\) earth days
2. \(124\) earth days
3. \(88\) earth days
4. \(225\) earth days
1. \(172\) earth days
2. \(124\) earth days
3. \(88\) earth days
4. \(225\) earth days
Subtopic: Kepler's Laws |
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Level 3: 35%-60%
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A wire of resistance \(R\) is cut into \(8\) equal pieces. From these pieces two equivalent resistance are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:
| 1. | \(\dfrac{R}{16}\) | 2. | \(\dfrac{R}{8}\) |
| 3. | \(\dfrac{R}{64}\) | 4. | \(\dfrac{R}{32}\) |
Subtopic: Combination of Resistors |
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A photon and an electron (of mass \(m\)) have the same total energy \(E. \) If \(c\) denotes the speed of light, what is the ratio of their de-Broglie wavelengths \((\lambda_{\text{photon}}/\lambda_{\text{electron}})\text{?} \)
| 1. | \(c\sqrt{\dfrac{2m}{E}} \) | 2. | \(\dfrac{1}{c}\sqrt{\dfrac{E}{2m}}\) |
| 3. | \(\sqrt{\dfrac{E}{2m}}\) | 4. | \(c\sqrt{2mE}\) |
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
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A sphere of radius \(R\) is cut from a larger solid sphere of radius \(2R\) as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the \(Y\)-axis is:
| 1. | \(\dfrac{7}{57}\) | 2. | \(\dfrac{7}{64}\) |
| 3. | \(\dfrac{7}{8}\) | 4. | \(\dfrac{7}{40}\) |
Subtopic: Moment of Inertia |
Level 3: 35%-60%
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An electron (mass \(9\times10^{-31}~\text{kg}\) and charge \(1.6\times10^{-19}~\text C\)) moving with speed \(c/100\) (\(c\)=speed of light) is injected into a magnetic field \(\vec B\) of magnitude \(9\times10^{-4}~\text{T}\) perpendicular to its direction of motion. We wish to apply an uniform electric field \(\vec E\) together with the magnetic field so that the electron does not deflect from its path. Then (speed of light \(c=3\times10^8~\text{ms}^{-1}\))
| 1. | \(\vec E\) is parallel to \(\vec B\) and its magnitude is \(27\times10^{2}~\text{V m}^{-1}\) |
| 2. | \(\vec E\) is parallel to \(\vec B\) and its magnitude is \(27\times10^{4}~\text{V m}^{-1}\) |
| 3. | \(\vec E\) is perpendicular to \(\vec B\) and its magnitude is \(27\times10^{4}~\text{V m}^{-1}\) |
| 4. | \(\vec E\) is perpendicular to \(\vec B\) and its magnitude is \(27\times10^{2}~\text{V m}^{-1}\) |
Subtopic: Lorentz Force |
Level 3: 35%-60%
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The electric field in a plane electromagnetic wave is given by \(E_z=60\cos(5x+1.5\times10^9t)~\text{V/m}.\) Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field):
| 1. | \(B_z=60\cos(5x+1.5\times10^9t)~\text T\) |
| 2. | \(B_y=60\sin(5x+1.5\times10^9t)~\text T\) |
| 3. | \(B_y=2\times10^{-7}\cos(5x+1.5\times10^9t)~\text T\) |
| 4. | \(B_x=2\times10^{-7}\cos(5x+1.5\times10^9t)~\text T\) |
Subtopic: Properties of EM Waves |
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A body weight \(48~\text{N}\) on the surface of the earth. The gravitational force experienced by the body due to the Earth at a height equal to one-third the radius of the Earth from its surface is:
| 1. | \(32~\text N\) | 2. | \(36~\text N\) |
| 3. | \(16~\text N\) | 4. | \(27~\text N\) |
Subtopic: Acceleration due to Gravity |
Level 3: 35%-60%
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An unpolarized light beam travelling in air is incident on a medium of refractive index \(1.73\) at Brewster's angle. Then:
| 1. | both reflected and transmitted light are perfectly polarized with angles of reflection and refraction close to \(60^\circ\) and \(30^\circ,\) respectively. |
| 2. | transmitted light is completely polarized with angle of refraction close to \(30^\circ\) |
| 3. | reflected light is completely polarized and the angle of reflection is close to \(60^\circ\) |
| 4. | reflected light is partially polarized and the angle of reflection is close to \(30^\circ\) |
Subtopic: Polarization of Light |
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