In a Cinema hall, the distance between the projector and the screen is increased by 2%. Then the intensity of illumination on the screen is
Answer: B
The illumination is decreased by about 4 per cent.
Intensity obeys the inverse-square law, \(I \propto 1/d^2\), so \[\frac{\Delta I}{I} = -2\,\frac{\Delta d}{d} = -2 \times 2\% = -4\%\] Doubling the distance would cut the illumination to a quarter.
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The capacity of a pure capacitor is 1 farad. In D.C circuit, its effective resistance will be
Answer: B
Its effective resistance in a DC circuit is infinite.
Capacitive reactance is \[X_C = \frac{1}{2\pi f C}\] and for direct current \(f = 0\), so \(X_C \rightarrow \infty\). Once the capacitor is charged no further current flows - a capacitor blocks DC and passes AC.
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To produce deflection in a television picture tube:
Answer: B
A magnetic field deflects the beam in a television picture tube.
Deflection coils around the neck of the tube sweep the electron beam across and down the screen. Magnetic deflection allows much wider deflection angles than electrostatic plates for the same tube length, which is why an oscilloscope uses plates but a television uses coils.
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Energy is continuously generated in the sun due to
Answer: A
The sun's energy comes from nuclear fusion.
Four hydrogen nuclei fuse to helium through the proton-proton chain: \[\mathrm{4\,^1_1H \rightarrow ^4_2He + 2e^+ + 2\nu + 26.7\ MeV}\] The mass of the helium nucleus is slightly less than that of the four protons, and the difference appears as energy by \(E = \Delta m c^2\).
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A ball is thrown vertically upwards. Assuming the air resistance to be constant and considerable:
Answer: A
The time of ascent is less than the time of descent.
Air resistance always opposes motion. Going up it acts downwards, so the retardation is \(g + a\) and the ball slows faster; coming down it acts upwards, so the acceleration is only \(g - a\). The larger effective acceleration on the way up means less time is spent there.
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Water kept in an earthen pot is less cool on rainy days than in summer because during the rainy days
Answer: C
Because the water that oozes out does not evaporate quickly, the air being already humid.
An earthen pot cools by evaporation of the water seeping through its pores, and evaporation draws latent heat from what remains. On a rainy day the air is close to saturation, so evaporation is slow and little heat is carried away.
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Which law is also called the law of inertia?
Answer: A
Newton's first law is the law of inertia.
It states that a body remains at rest or in uniform motion in a straight line unless an external force acts on it, so it defines inertia and identifies the inertial frames in which the other two laws hold.
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The image of an object formed on the retina of the eye is
Answer: C
The image on the retina is real and inverted.
The eye's lens is convex and the object lies beyond its focal length, so the rays actually converge on the retina, forming a real image, and it is upside down and left-right reversed. The brain learns to interpret it the right way up.
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A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of the emf's is :
Answer: D
The ratio of the emfs is 3 : 2.
With the cells assisting, the balancing length measures \(E_1 + E_2\); with them opposing, it measures \(E_1 - E_2\).
\[\frac{E_1+E_2}{E_1-E_2} = \frac{50}{10} = 5\]
\[5E_1 - 5E_2 = E_1 + E_2 \Rightarrow 4E_1 = 6E_2 \Rightarrow \frac{E_1}{E_2} = \frac{3}{2}\]
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Why does not the hydrogen atom emit X-rays?
Answer: C
Because its energy levels lie very close together.
X-rays are emitted when an electron falls into a vacancy in an inner shell of a heavy atom, where the binding energies are thousands of electron-volts. Hydrogen has a single electron and its largest transition energy is only 13.6 eV, which lies in the ultraviolet.
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