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Consider two satellites S₁ and S₂ with periods of revolution 1 hr and 8 hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S₁ to the angular velocity of satellite S₂ is

a. 8: 1 b. 1: 8 c. 2: 1 d. 1: 4 Answer: (a) We know that ω = 2... View Article

Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be

a. \(\begin{array}{l}\sqrt{\frac{(1+2\sqrt{2})G}{2}}\end{array} \) b. \(\begin{array}{l}\sqrt{G(1+2\sqrt{2})}\end{array} \) c. \(\begin{array}{l}\sqrt{\frac{G}{2}(2\sqrt{2}-1)}\end{array} \) d. \(\begin{array}{l}\sqrt{\frac{G}{2}(1+2\sqrt{2})}\end{array} \) Answer: (a) ⇒ By resolving force F2, we... View Article

The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, D = 1.25 × 10⁻² m rise of water, h = 1.45 × 10⁻² m. Using g = 9.80 m/s² and the simplified relation T = [rhg / 2] × 10³ N / m, the possible error in surface tension is closest to:

1) 0.15% 2) 1.5% 3) 2.4% 4) 10% Answer: (2) [ΔT / T] * 100 = [ΔD / D] *... View Article

Which of the following statements is false?

1) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude. 2)... View Article

In amplitude modulation, sinusoidal carrier frequency used is denoted by ω_c and the signal frequency is denoted by ω_m. The bandwidth (∆ω_m) of the signal is such that ∆ω_m<< ω_c. Which of the following frequencies is not contained in the modulated wave?

1) ωm 2) ωc 3) ωm + ωc 4) ωc − ωm Answer: (1) Modulated wave has a frequency range.... View Article

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be:

1) 45o 2) 90o 3) 135o 4) 180o Answer: (4) In common emitter configuration for the n-p-n transistor, the phase... View Article

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by:

1) t = (T / 2) (log 2 / log 1.3) 2) t = (T) (log 1.3 / log 2)... View Article

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = λ₁ / λ₂, is given by:

1) r = 4/3 2) r = 2/3 3) r = 3/4 4) r = 1/3 Answer: (4) From energy... View Article

A particle A of mass m and initial velocity v collides with a particle B of mass m / 2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λ_A to λ_B after the collision is:

1) λA / λB = 1/3 2) λA / λB = 2 3) λA / λB = 2/3 4) λA... View Article

In Young’s double-slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is:

1) 1.56 mm 2) 7.8 mm 3) 9.75 mm 4) 15.6 mm Answer: (2) For λ1, y = mλ1D /... View Article

A diverging lens with a magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of the magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is:

1) real and at a distance of 40 cm from the convergent lens. 2) virtual and at a distance of... View Article

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If λ_min is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ_min with log V is correctly represented in:

Answer: (1) In X-ray tube λmin = hc / eV In λmin = ln (hc / e) – ln V... View Article

In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

1) 200 Wb 2) 225 Wb 3) 250 Wb 4) 275 Wb Answer: (3) ϵ = dɸ / dt iR... View Article

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full-scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 − 10 V is:

1) 1.985 × 103 Ω 2) 2.045 × 103 Ω 3) 2.535 × 103 Ω 4) 4.005 × 103 Ω... View Article

A magnetic needle of magnetic moment 6.7 × 10⁻² Am² and moment of inertia 7.5 × 10⁻⁶ kg m² is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

1) 6.65 s 2) 8.89 s 3) 6.98 s 4) 8.76 s Answer: (1) T = 2π √I / MB... View Article

In the the below given circuit diagram the current in each resistance is:

1) 1 A 2) 0.25 A 3) 0.5 A 4) 0 A Answer: (4) The potential difference in each loop... View Article

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:

1) CE 2) CE (r1 / r2 + r) 3) CE (r2 / r + r2) 4) CE (r1 /... View Article

A capacitance of 2 µF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 µF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:

1) 2 2) 16 3) 24 4) 32 Answer: (4) The following arrangement will do the needful: 8 capacitors of... View Article

An electric dipole has a fixed dipole moment p, which makes angle θ with respect to the x-axis. When subjected to an electric field E₁= E_i, it experiences a torque T₁= τ k. When subjected to another electric field E₂ = √3 E₁j it experiences a torque T₂ = – T₁. The angle θ is:

1) 30o 2) 45o 3) 60o 4) 90o Answer: (3) p = p cos θ i + p sin θ... View Article

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 × 10⁸ ms⁻¹)

1) 10.1 GHz 2) 12.1 GHz 3) 17.3 GHz 4) 15.3 GHz Answer: (3) For relativistic motion f = fo... View Article

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