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A carnot engine operates between two reservoirs of temperature 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy in(J ) delivered by the engine to the low temperature reservoir, in a cycle, is

Answer: (600) η = 1 – (T2/T1) = 1- (300/900) =2/3 Given, W = 1200 J From conservation of energy... View Article

A loop ABCDEFA of straight edges has six corner points A(0,0,0), B(5,0,0), C(5,5,0), D(0,5,0), E(0,5,5), F(0,0,5). The magnetic field in this region is B˙ = (3ˆi + 4kˆ) T. The quantity of flux through the loop ABCDEFA (in Wb) is

Answer: (175) As we know, magnetic flux = \(\begin{array}{l}\vec{B}\times \vec{A}\end{array} \) ⇒ (Bx + Bz) • (Ax + Az) ⇒... View Article

A non- isotropic solid metal cube has coefficient of linear expansion as 5 × 10⁻⁵/^◦C along the x-axis and 5 × 10⁻⁶/^◦C along y-axis and z-axis. If the coefficient of volumetric expansion of the solid is C × 10⁻⁶/^◦C then the value of C is

Answer: (60) We know that, V = xyz ∆v/v = (∆x/x) + (∆y/y) + (∆z/z) (1/T)∆v/v = (1/T)((∆x/x)+(∆y/y)+(∆z/z)) y =... View Article

A parallel plate capacitor has plates of area A separated by distance ‘d’ between them. It is filled with a dielectric which has a dielectric constant varies as k (x) = k(1 + αx), where ‘x’ is the distance measured from one of the plates. If (αd <<1), the total capacitance of the system is best given by the expression:

a.\(\begin{array}{l}\frac{A\epsilon _{0}k}{d}\left [ 1+(\frac{\alpha d}{2})^{2}\right ]\end{array} \) b.\(\begin{array}{l}\frac{A\epsilon _{0}k}{d}\left [ 1+(\frac{\alpha d}{2})\right ]\end{array} \) c.\(\begin{array}{l}\frac{A\epsilon _{0}k}{d}\left [ 1+(\frac{\alpha^{2} d}{2})\right ]\end{array}... View Article

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... 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... 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 =... 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... 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... 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. \(\begin{array}{l}5m\left[u^{2}-\frac{119}{200}\frac{GM}{R}\right]\end{array} \) b. \(\begin{array}{l}\frac{m}{20}\left [ u-\sqrt{\frac{2GM}{3R}} \right ]^{2}\end{array} \) c. \(\begin{array}{l}\frac{3m}{8}\left [ u+\sqrt{\frac{5GM}{6R}} \right ]^{2}\end{array} \) d. \(\begin{array}{l}\frac{m}{20}\left [... 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... 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... 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... 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... 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 ×... 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. \(\begin{array}{l}\frac{\sigma }{2\epsilon _{0}}\left [ (1-\frac{\sqrt{3}}{2})\hat{y}-\frac{1}{2}\hat{x}) \right ]\end{array} \) b. \(\begin{array}{l}\frac{\sigma }{2\epsilon _{0}}\left [ (1+\frac{\sqrt{3}}{2})\hat{y}-\frac{1}{2}\hat{x}) \right ]\end{array} \) c. \(\begin{array}{l}\frac{\sigma... 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... 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... 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 =... 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... View Article

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