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In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5×10^-12 m, the minimum electron energy required is close to :

a. 1 keV b. 25 keV c. 500 keV d. 100 keV Answer: b Given λ = 7.5×10-12 h = λ = h/P P = h/λ KE = P2/2m =... View Article

In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 1/40 rad by using light of wavelength λ₁. When the light of wavelength λ₂is used a bright fringe is seen at the same at the same angle in the same set up. Given that λ₁and λ₂are in visible range (380 nm to 740 nm), their values are :

a. 380 nm, 525 nm b. 625 nm, 500 nm c. 380 nm, 500 nm d. 400 nm, 500 nm Answer: b Path difference = d sinθ = dθ (approx) =... View Article

A plano convex lens of refractive index μ₁ and focal length f₁ is kept in contact with another plano concave lens of refractive index μ₂ and focal length f₂. If the radius of curvature of their spherical faces is R each and f₁ = 2f₂, then μ₁ and μ₂ are related as :

a. μ1 + μ2 = 3 b. 2μ2- μ1 = 1 c. 2μ1- μ2 = 1 d. 3μ2- 2μ1 = 1 Answer: c Given f1 = 2f2 (1/2f2) = (1/f1) =... View Article

If the magnetic field of a plane electromagnetic wave is given by (The speed of light =3×10⁸ m/sec) [latex]B = 100times 10^{-6}sin left ( 2pi times 2times 10^{15} (t-frac{x}{c})right )[/latex] then the maximum electric field associated with it is

a. 4×104 N/C b. 6×104 N/C c. 3×104 N/C d. 4.5×104 N/C Answer: c E0 = B0×C = 100×10-6×3×108 = 3×104N/C... View Article

A magnet of total magnetic moment [latex]10^{-2}hat{i}[/latex] A-m² is placed in a time-varying magnetic field, [latex]Bhat{i}(cos omega t)[/latex] where B = 1 Tesla and ω= 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is

a. 0.007 J b. 0.02 J c. 0.01 J d. 0.028 J Answer: b Work done, W = = 2×10-2×1 cos(0.125) = 0.02 J... View Article

An insulting thin rod of length l has a linear charge density [latex]rho (x)= rho _{0}frac{x}{l}[/latex] on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :

a. (π/4)nρl3 b. nρl3 c. πnρl3 d. (π/3)nρl3 Answer: a Since M = NIA dq = λdx and A = πx2... View Article

A solid metal cube of edge length 2 cm is moving in the positive y direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z direction. The potential difference between the two faces of the cube perpendicular to the x axis, is :

a. 1 mV b. 6 mV c. 12 mV d. 2 mV Answer: c The potential difference between two faces perpendicular to x axis will be... View Article

In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R₁, and R₂ respectively, are:

a. 2,2 b. 0,1 c. 1,2 d. 0.5,0 Answer: d i1 = 10/20 = 0.5 A i2 = 0... View Article

A uniform metallic wire of resistance 18 ohm is bent to form an equilateral triangle. The resistance across any two vertices of the triangle is (in ohm).

a. 8 ohm b. 12 ohm c. 4 ohm d. 2 ohm Answer: c Let Req be resistance between any two vertex. 1/Req = (1/12)+(1/6) So Req = 4 ohm... View Article

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a< b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be :

a. b. c. d. Answer: b Potential at point P, V = Since Qa : Qb : Qc : :a 2 : b2: c2 Since σa = σb = σc So Qa =... View Article

Two electric dipoles, A,B with respective dipole moments [latex]vec{d_{A}}=-4qahat{i}[/latex] and [latex]vec{d_{B}}=-2qahat{i}[/latex] placed on the x-axis with a separation R, as shown in the figure.

The distance from A at which both of them produce the same potential is: a. b. c. d. Answer: a V = 4qa/(R+x) = 2qa/x2... View Article

A parallel plate capacitor is of area 6 cm² and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant K₁=10, K₂ = 12 and K₃ =14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

a. 34 b. 12 c. 4 d. 14 < strong>Answer: b Let K be the dielectric constant of the material used. So So K = 36/3 = 12... View Article

A train moves towards a stationary observer with speed 34m/s. The train sounds a whistle and its frequency registered by the observer is f₁. If the train’s speed is reduced to 17m/s, the frequency registered is f₂. If the speed of sound of 340m/s, then the ratio f₁/f₂is

a. 18/7 b. 21/20 c. 20/19 d. 19/18 Answer: d f1 = f(v/v-vs) = f(340/340-34) = f(340/306) f2 = f(340/340-17) = f(340/323) f1/f2 =... View Article

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The siring is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to __?

a. 10 cm b. 16.6 cm c. 20 cm d. 33.3 cm Answer: c The velocity of wave on string, V = √(T/μ) = √(8×1000/5) = 40 m/s The wavelength... View Article

A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 WK^-1m^-1, the energy flux through it in steady state is :

a. 90 W/m2 b. 120 W/m2 c. 65 W/m2 d. 200 W/m2 Answer: a (dQ/dt) = kAΔt/l (1/A)(dQ/dt) = (0.1×900)/1 = 90W/m2... View Article

Three Carnot engines operate in series between a heat source at a temperature T₁ and a heat sink at temperature T₄ (see figure). There are two other reservoirs at temperature T₂ and T₃, as shown, with T₁ >T₂ >T₃ >T₄. The three engines are equally efficient if :

a. T2 = (T1T42)1/3 ; T3 = (T12 T4)1/3 b. T2 = (T1T4)1/2 ; T3 = (T12 T4)1/3 c. T2 = (T12 T4)1/3 ; T3 = (T1 T42)1/3 d. T2 = (T13 T4)1/4 ;... View Article

Water flows into a large tank with flat bottom at the rate of 10⁻⁴m³s⁻¹. Water is also leaking out of a hole of area 1 cm² at its bottom. If the height of the water in the tank remains steady, then this height is

a. 5.1 cm b. 4 cm c. 2.9 cm d. 1.7 cm Answer: a Water inflow rate = water outflow rate Water inflow rate = 10-4 Water outflow rate =... View Article

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

a. (1/2)mv2 b. mv2 c. (3/2)mv2 d. 2mv2 Answer: b Orbital velocity = v Escape velocity = Ve v = √(GM/R) g = GM/R2 gR2 = GM v = √gR... View Article

To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and the floor is μ, the torque, applied by the machine on the mop is :

a. μFR/6 b. μFR/3 c. μFR/2 d. 2μFR/3 Answer: d Force per unit length = F/πR2)2πxdx Torque = F×r = = = =... View Article

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

a. 2F/3mR b. 3F/2mR c. F/3mR d. F/2mR Answer: a Considering pure rolling, acm = Rα FR = (mR2 +(1/2) mR2 ) α =... View Article