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A bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from the rest, the bob starts falling vertically. When it has covered a distance h, the angular speed of the wheel will be:

a. r√3/4gh b. (1/r)√4gh/3 c. ( r√3)/2gh d. (1/r)√2gh/3 Answer: (b) By energy conservation, mgh = (1/2) mv2 + (1/2)Iω ⇒gh = v2/2 +ω2r2/4... View Article

1 liter of dry air at STP expands adiabatically to a volume of 3 litres. If γ = 1.4, the work done by air is (31.4 = 4.655) (take air to be an ideal gas)

a. 48 J b. 100.8 J c. 90.5 J d. 60.7 J Answer: (c) Given, P1 = 1 atm, T1 = 273 K (At STP) In adiabatic process, P1V1γ = P2V2γ P2 = 1... View Article

Speed of transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90m/s. If the Young’s modulus of wire is 16 × 10¹¹Nm⁻², the extension of wire over its natural length is

a. 0.03 mm b. 0.04 mm c. 0.02 mm d. 0.01 mm Answer: (a) Given, M = 6 grams = 6 × 10−3 kg L = 60 cm = 0.6 m A = 1 mm2 = 1 × 10−6m2 Using... View Article

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece should be close to:

a. 22 mm b. 12 mm c. 2 mm d. 33 mm Answer: (a) Magnification of compound microscope for least distance of distinct vision setting (strained... View Article

Three point particles of mass 1 kg, 1.5 kg and 2.5 kg are placed at three corners of a right triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of the system is at the point:

a. 0.9 cm right and 2.0 cm above 1 kg mass b. 2.0 cm right and 0.9 cm above 1 kg mass c. 1.5 cm right and 1.2 cm above 1 kg mass d. 0.6 cm... View Article

A satellite of mass m is launched vertically upward with an initial speed u from the surface of the earth. After it reaches height R(R = radius of earth), it ejects a rocket of mass m/10 so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G = gravitational constant; M is the mass of earth)

a. b. c. d. Answer: (a) T.Eground= T.ER (1/2)mu2 + (-GMm/R) = (1/2)mv2 +(-GMm/2R) (1/2)mv2 = (1/2)mu2+(-GMm/2R) v2 = u2+(-GMm/R)... View Article

The radius of gyration of a uniform rod of length l about an axis passing through a point l/4 away from the center of the rod, and perpendicular to it, is

a. √ (7/48)l b. √ (3/8) l c. (1/4) l d. (1/8) l Answer: (a) Moment of inertia of rod about axis perpendicular to it passing through its... View Article

Visible light of wavelength 6000 × 10⁻⁸cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minima is at 60^o from the central maxima. If the first minimum is produced at θ₁, then θ₁ is close to

a. 20o b. 45o c. 30o d. 25o Answer: (d) For single slit diffraction experiment: Angle of minima are given by sin θn = nλ/d (sin θn ≠ θn as... View Article

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant ’b’, the correct equivalence will be

a. L ↔ 1/b, C ↔ 1/m, R ↔ 1/k b. L ↔ k, C ↔ b, R ↔ m c. L ↔ m, C ↔ k, R ↔ b d. L ↔ m, C ↔ 1/k , R ↔ b Answer: (d) For damped oscillator by... View Article

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 10⁻¹⁶s. The frequency of revolution of the electron in its first excited state (in s⁻¹) is

a. 6.2 × 1015 b. 7.8 × 1014 c. 1.6 × 1014 d. 5.6 × 1012 Answer: (b) Time period is proportional to n3 /Z2 Let T1 be the time period in... View Article

If the magnetic field in a plane electromagnetic wave is given by B˙ = 3 × 10⁻⁸sin(1.6 × 10³x + 48 × 10¹⁰t)ˆj T then what will be expression for electric field?

a. E˙ = 3 × 10−8sin(1.6 × 103x + 48 × 1010t)ˆi V/m b. E˙ = 3 × 10−8sin(1.6 × 103x + 48 × 1010t)ˆj V/m c. E˙ = 60 sin(1.6 × 103x + 48 × 1010t)kˆ... View Article

Two infinite planes each with uniform surface charge density +σ C/m² are kept in such a way that the angle between them is 30^o. The electric field in the region shown between them is given by:

a. b. c. d. Answer: (a) Field due to single plate =... View Article

The current (in A) flowing through 1 Ω resistor in the following circuit is

a. 0.40 A b. 0.25 A c. 0.20 A d. 0.5 A Answer: (c) Net resistance across CD = 1/2 Ω Net resistance across BE = 2 + (1/2) = (5/2) Ω Net... View Article

Consider a circular coil of wire carrying current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by φ_i The magnetic flux through the area of the circular coil area is given by φ₀.

Which of the following option is correct? a. φi= −φo b. φi>φo c. φi<φo d. φi=φo Answer: (a) As magnetic field line of ring will... View Article

Two moles of an ideal gas with Cp/Cv = 5/3 are mixed with 3 moles of another ideal gas with Cp/Cv = 4/3. The value of Cp/Cv for the mixture is

a. 1.47 b. 1.4 c. 1.42 d. 1.50 Answer: (c) For γ = Cp/Cv = 5/3 Using formula Cp = Rγ/γ-1 Cv = R/γ-1 Cp = 5R/2 Cv = 3R/2 Similarly for... View Article

A long solenoid of radius R carries a time (t) dependent current I(t) = I₀t(1 − t). A ring of radius 2R is placed coaxially near its middle. During the time instant 0 ≤ t ≤ 1, the induced current (IR) and the induced EMF (V_R) in the ring changes as:

a. Direction of IR remains unchanged and VR is maximum at t = 0.5 b. Direction of IR remains unchanged and VR is zero at t = 0.25 c. At t = 0.5... View Article

A 60 HP electric motor lifts an elevator with a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to (Given 1 HP = 746 W, g = 10 m/s²)

a. 1.5 m/s b. 1.7 m/s c. 2.0 m/s d. 1.9 m/s Answer: (d) P = Fv + Mgv Applied power = 4000 × v + 20000 v 60 × 246 = 4000 v +... View Article

Which of the following gives reversible operation?

Answer: (c) Since, there is only one input hence the operation is reversible.... View Article

A polarizer-analyzer set is adjusted such that the intensity of light coming out of the analyzer is just 10 % of the original intensity. Assuming that the polarizer-analyzer set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is

a. 45o b. 90o c. 71.6o d. 18.40 Answer: (d) Intensity after polarisation through polaroid = Iocos2φ So, 0.1Io = Iocos2φ ⇒cosφ = √0.1... View Article

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm⁻² and it is absorbed by the water over an effective area of 0.05 m². Assuming that the heat loss from the water to the surroundings is governed by Newton’s law of cooling, the difference (in ℃) in the temperature of water and the surroundings after a long time will be _____________.

(Ignore the effect of the container, and take constant for Newton’s law of cooling = 0.001 s−1, the Heat capacity of water = 4200 J... View Article