Archives

Economy This Week (17th Jul to 23rd Jul 2021)

Economy is an important part of the UPSC prelims and mains exams; this series titled ‘Economy This Week’ has been initiated to address the need... View Article

26 July 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 26th Jul 2021. Important news and views to boost... View Article

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be:

a. b. c. d. Answer: (a) We know that ωf = Ai = A Also, momentum is conserved just before and just after the block of... View Article

In Young’s double-slit experiment, the width of one of the slits is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

a. 4: 1 b. 2: 1 c. 3: 1 d. 1: 4 Answer: (a) Given: w2 = 3w1 Also, A ∝ w w1 / w2 = ⅓ ... (1) Assume w1 = x, w2 = 3x We know that... View Article

If an emitter current is changed by 4mA, the collector current changes by 3.5 mA. The value of β will be:

a. 7 b. 0.875 c. 0.5 d. 3.5 Answer: (1) Given: ΔIE = 4 mA ΔIC = 3.5 mA We know that, α = ΔIC / ΔIE ⇒... View Article

The work done by a gas molecule in an isolated system is given by, [latex]alpha cdot beta ^{2}cdot e^{-frac{x^{2}}{alpha .KT}}[/latex], where x is the displacement, k is the Boltzmann constant and T is the temperature.α and β are constants. Then the dimensions of β will be:

a. [M0LT0] b. [M2LT2] c. [MLT–2] d. [ML2T–2] Answer: (c) Given: work done = k = boltzmann constant T = temperature x =... View Article

Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as:

I1 = M.I. of thin circular ring about its diameter, I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,... View Article

The focal length f is related to the radius of curvature r of the spherical convex mirror by:

a. f = r b. f = - ½ r c. f = +½ r d. f = – r Answer: (c) So, r / 2 = f f = +½ r... View Article

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E. The transition A, B and C respectively represents:

a. The series limit of Lyman series, third member of Balmer series and second member of Paschen series b. The first member of the Lyman... View Article

A current through a wire depends on time as i = α₀t + βt² where α₀ = 20 A/s and β = 8 As^-2. Find the charge crossed through a section of the wire in 15 s.

a. 2100 C b. 260 C c. 2250 C d. 11250 C Answer: (d) Given: i = α0t + βt2 α = 20 A/s and β = 8As-2 t = 15 sec... View Article

Given below are two statements:

Statement-I: Two photons having equal linear momenta have equal wavelengths. Statement-II: If the wavelength of a photon is decreased, then the... View Article

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

Answer: (a) a= dv / d t= slope of (v – t) curve If m = +ve, then equation of straight line is y = mx + c ⇒ v = mt + c (for MB)... View Article

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is

a. b. c. d. Answer: (a) ⇒ G(m)(2m) / d2 = mω2 × 2d / 3 ⇒ 2Gm / d2 = ω2 × 2d / 3 ⇒... View Article

If Y, K and η are the values of Young’s modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

a. b. c. d. Answer: (a) ⇒ Y = 3K (1 – 2σ) ⇒ σ = ½ (1 - Y / 3K) .... (1) ⇒Y = 2η (1 +... View Article

A cell E₁ of emf 6V and internal resistance 2Ω is connected with another cell E₂ of emf 4V and internal resistance 8Ω (as shown in the figure). The potential difference across points X and Y is

a. 3.6V b. 10.0V c. 5.6V d. 2.0V Answer: (c) emf of E1 = 6V r1 = 2 Ω emf of E2= 4V r2 = 8Ω |vx– vy| = potential... View Article

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be

a. 2: 1 b. 1: 4 c. 4: 1 d. 1: 2 Answer: (b) Given that first connection Second connection C34 = C + C = 2 C Now, the ratio of... View Article

n moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes:

A→ B: Isothermal expansion at temperature T so that the volume is doubled from V1 to V2 and pressure changes from P1 to P2. B → C:... View Article

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 /T Given: Ratio of time period T1 / T2 = 1/8 ⇒ ω ∝... 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. b. c. d. Answer: (a) ⇒ By resolving force F2, we get ⇒ F1 + F2 cos 45° + F2 cos 45° = Fc ⇒ F1 + 2F2... 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] * 100 + [Δh / h] * 100 = (0.01 / 1.25) * 100 = (0.01 / 1.45) * 100... View Article