Assuming the sun to have a spherical outer surface of radius \(r,\) radiating like a black body at temperature \(t^\circ \text{C},\) the power received by a unit surface of the earth (normal to the incident rays) at a distance \(R\) from the centre of the sun will be:
(where \(\sigma\) is Stefan's constant)
| 1. | \(\dfrac{4\pi r^2\sigma t^4}{R^2}\) | 2. | \(\dfrac{r^2\sigma(t+273)^4}{4\pi R^2}\) |
| 3. | \(\dfrac{16\pi^2r^2\sigma t^4}{R^2}\) | 4. | \(\dfrac{r^2\sigma(t+273)^4}{R^2}\) |
A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are (, \(3).\) The path of the particle makes an angle of __________ with the \(x\)-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)
1. \(6.0\) Fermi
2. \(9.6\) Fermi
3. \(12.0\) Fermi
4. \(4.8\) Fermi
A wheel has an angular acceleration of \(3.0\) rad/s2 and an initial angular speed of \(2.0\) rad/s. In a time of \(2\) s, it has rotated through an angle (in radians) of:
| 1. | \(6\) | 2. | \(10\) |
| 3. | \(12\) | 4. | \(4\) |
The resistance of an ammeter is 13 Ω and its scale is graduated for a current up to 100 A. After an additional shunt has been connected to this ammeter, it becomes possible to measure currents up to 750 A by this ammeter. The value of shunt resistance is:
1. 20
2. 2
3. 0.2
4. 2 k
Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion:
1. depends on v and not on R.
2. depends on both R and v.
3. is independent of both R and v.
4. Depends on R and not on v.
1. \(90~\text{V}\)
2. \(120~\text{V}\)
3. \(220~\text{V}\)
4. \(30~\text{V}\)
Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure.
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)
A uniform rod \(AB\) of length \(l\) and mass \(m\) is free to rotate about point \(A\). The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about \(A\) is \(\dfrac{ml^2}{3}\) the initial angular acceleration of the rod will be:
1. \(\dfrac{2g}{3l}\)
2. \(\dfrac{mgl}{2}\)
3. \(\dfrac{3}{2}gl\)
4. \(\dfrac{3g}{2l}\)
The frequency of a light wave in a material is 2×1014 Hz and the wavelength is 5000 Å. The refractive index of the material will be:
1. 1.40
2. 1.50
3. 3.00
4. 1.33
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