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Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ(r) = A + Br. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is

a. b. c. d. Answer: (a) = A + Br ∫dm = ∫(A+Br) 2πrdr I = ∫dm r2 = ∫0a(A+Br)2πr3dr = 2 π(A (a4/4) + B(a5/5)) = 2π a4 (A/4) + Ba/5)... View Article

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45° with the vertical. Then F equals (Take g = 10 m/s² and rope to be massless)

a. 100 N b. 90 N c. 75 N d. 70 N Answer: (a) Equating the vertical and horizontal components of the forces acting at point T/√2 = 100... View Article

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecules changes from τ₁ to τ₂. If C_p/C_v = γ for this gas, then a good estimate for τ₂ /τ₁is given by

a. 1/2 b. (1/2) (γ +1)/2 c. (1/2) γ d. 2 Answer: (b) Relaxation time (τ) dependence on volume and temperature can be given by τ ∝ V/√T.... View Article

In a building, there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of and 2 heaters of 1kW. The voltage of electric main is 220V. The minimum fuse capacity (rated value) of the building will be approximately

a. 10 A b. 20 A c. 25 A d. 15 A Answer: (b) Total power consumption of the house (P) = Number of appliances ×Power rating of each appliance... View Article

A box weighs 196 N on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10m/s² at the North Pole and radius of the Earth = 6400 km )

a. 194.32 N b. 194.66 N c. 195.32 N d. 195.66 N Answer: (c) Weight of the object at the pole,W = mg = 196 N Mass of the object, m = w/g =... View Article

RPSC RAS Main Exam 2023 Postponed

The RPSC RAS Main Exam 2023 has been postponed to July 20 and 21, 2024. It was earlier scheduled to be held on January 27 and 28, 2024. This is... View Article

16 July 2021: UPSC Exam Comprehensive News Analysis

CNA 16th July 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND GOVERNANCE 1. Why do you need the ‘colonial... View Article

15 July 2021: PIB Summary & Analysis

TABLE OF CONTENTS 1. World Youth Skills Day 2. K. Kamaraj 3. PRASHAD Scheme 4. Central Board of Indirect Taxes & Customs (CBIC) 5. Raksha... View Article

Which of the following is a scalar quantity?

1) Displacement 2) Electric field 3) Acceleration 4) Work Answer: 4) Work Solution: Displacement, electrical field and acceleration... View Article

Any vector in an arbitrary direction can always be replaced by two (or three)

1) Parallel vectors which have the original vector as their resultant 2) Mutually perpendicular vectors which have the original vector as their... View Article

Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be

1) Zero 2) 10 N 3) 20 N 4) 10√2 N Answer: 1) Zero Solution: If the angle between all forces which are equal and lying in... View Article

100 coplanar forces each equal to 10 N act on a body. Each force makes an angle π/50 with the preceding force. What is the resultant of the forces?

1) 1000 N 2) 500 N 3) 250 N 4) Zero Answer: 4) Zero Total angle=100x (π/50)=2π All the forces will pass through one point and... View Article

A hail has the dimensions 10 m x 12 m x 14 m. A fly starting at one corner ends up at a diagonally opposite corner. What is the magnitude of its displacement?

1) 17 m 2) 26 m 3) 36 m 4) 21 m Answer: 4) 21 m Solution: The magnitude of displacement d = √440 d = 2√110 d = 20. 97 m... View Article

A force of 5 N acts on a particle along a direction making an angle of 60^o with vertical. Its vertical component will be

1) 10N 2) 3N 3) 4N 4) 2.5N Answer: 4) 2.5N Solution: The component of force in the vertical direction = F cosθ = F cos 600 = 5 x (1/2)... View Article

Two trains along the same straight rails moving with constant speed 60 km/hr and 30 km/hr respectively towards each other. If at time t. = 0, the distance between them is 90 km, the time when they collide is

1) 1 hr 2) 2 hr 3) 3 hr 4) 4 hr Answer: 1) 1 hr Solution: Let the two trains be Train A and Train B Speed of train A = 30 km/hr Speed of... View Article

Assertion The minimum number of non-coplanar vectors whose sum can be zero is four. Reason The resultant of two vectors of unequal magnitude can be zero.

Assertion The minimum number of non-coplanar vectors whose sum can be zero is four. Reason The resultant of two vectors of unequal magnitude can... View Article

Assertion: Two vectors are said to be like vectors if they have the same direction but different magnitude. /Reason: Vector quantities do not have a specific direction.

Assertion: Two vectors are said to be like vectors if they have the same direction but different magnitude. Reason: Vector quantities do not... View Article

Assertion: The sum of two vectors can be zero. Reason: The vector cancels each other when they are equal and opposite.

Assertion: The sum of two vectors can be zero. Reason: The vector cancels each other when they are equal and opposite. 1) both Assertion and... View Article

Assertion A physical quantity cannot be called a vector if its magnitude is zeroReason A vector has both, magnitude and direction.

Assertion A physical quantity cannot be called a vector if its magnitude is zero Reason A vector has both, magnitude and direction. 1) If both... View Article

Assertion A null vector is a vector whose magnitude is zero and direction is arbitraryReason A null vector does not exist.

Assertion A null vector is a vector whose magnitude is zero and direction is arbitrary Reason A null vector does not exist. 1) If both... View Article