# 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, $alpha cdot beta ^{2}cdot e^{-frac{x^{2}}{alpha .KT}}$, 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