Physics
- A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μ_s. The maximum safe velocity on this road is : Answer: 2. √(gRμ_s+tanθ/1-μ_stanθ) Key idea: at maximum speed friction acts down the slope, along with the normal reaction. Vertical: Ncosθ=... 1
- Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]Column 1: (A) m = -2; (B) m = -1/2; (C) m = +2; (D) m = +1/2Column 2: (a) Convex mirror; (b) Concave mirror; (c) Real image; (d) Virtual i… Answer: 1. A → b and c; B → b and c; C → b and d; D → a and d Key idea: real images have negative m (inverted); virtual images have positive... 1
- A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance : Answer: 4. 54.0 cm Key idea: the objective forms an image of the nearby object; the eyepiece must focus on that image (final image at infini... 1
- Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the… Answer: 4. \1+(n-1)p\ρ Key idea: weight of cylinder equals total buoyant force. Length pL is in the denser liquid ( nρ ); remaining (1-p)L i... 1
- A piece of ice falls from a height h so that it melts completely. Only one - quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is : [Latent heat of ice is 3.4×10^5 J/kg… Answer: 3. 136 km Key idea: loss in potential energy mgh becomes heat; one-quarter of it melts the ice. 1/4mgh=mL⇒ h=4L/g=dfrac4×3.4×10⁵10=1... 1
- A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then : Answer: 2. Compressing the gas through adiabatic process will require more work to be done. Key idea: compare areas under the P-V curves. Fo... 1
- A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t^2 j) N, where i and j are unit vectors along x and y axis. What power will be developed by the force at the time t ? Answer: 4. (2t³ + 3t⁵) W Key idea: power P=vec F·vec v ; find vec v by integrating vec a=vec F/m . vec a=2that i+3t²hat j (m = 1 kg), so vec... 1
- When an α-particle of mass 'm' moving with velocity 'v' bombards on a heavy nucleus of charge 'Ze', its distance of closest approach from the nucleus depends on m as : Answer: 1. 1/m Key idea: at the closest approach all kinetic energy becomes electrostatic potential energy. 1/2mv²=k(2e)(Ze)/r₀⇒ r₀=4kZe²/mv... 1
- The charge flowing through a resistance R varies with time t as Q = at - bt^2, where a and b are positive constants. The total heat produced in R is : Answer: 1. a³R/6b Key idea: current I=dQ/dt ; heat H=∫ I²R dt . I=a-2bt , which becomes zero at t=a/2b . H=R∫₀^(a/2b)(a-2bt)²dt=R[-(a-2bt)³/... 1
- An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is : (c being velocity of light) Answer: 1. 1/c(E/2m)^(1/2) Key idea: use λ=h/p for the electron and λ=hc/E for the photon. Electron: p=√(2mE) , so λ_e=h/√(2mE) . Photon: λ_... 1
- Out of the following options which one can be used to produce a propagating electromagnetic wave ? Answer: 4. An accelerating charge Key idea: electromagnetic waves are produced by accelerated (time-varying) charges. A charge at constant v... 1
- Consider the junction diode as ideal. The value of current flowing through AB is : Answer: 2. 10⁻² A Key idea: check whether the ideal diode is forward or reverse biased. A is at +4 V (on the p-side) and B at -6 V, so the d... 1
- A npn transistor is connected in common emitter configuration in a given amplifier. A load resistance of 800 Ω is connected in the collector circuit and the voltage drop across it is 0.8 V. If the current amplification factor is 0.96 and the input re… Answer: 1. 4, 3.84 Key idea: in common emitter, A_v=βR_L/R_i and power gain =β A_v . The question uses 0.96 as the current gain β in these f... 1
- Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a… Answer: 3. v ∝ x^(-1/2) Key idea: at equilibrium, the electric force balances the horizontal component of tension. With tanθ≈x/2l : kq²/x²=m... 1
- A capacitor of 2\ μ F is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is : Answer: 4. 80% Key idea: charge is conserved; it is shared between the capacitors until the potentials are equal, and the difference in ener... 1
- At what height from the surface of earth the gravitation potential and the value of g are -5.4×10^7\ J kg^-2 and 6.0\ ms^-2 respectively ? Take the radius of earth as 6400 km : Answer: 1. 2600 km Key idea: V=-GM/r and g=GM/r² , so r=|V|/g . r=dfrac5.4×10⁷6.0=9.0×10⁶ m =9000 km. Height h=r-R_E=9000-6400=2600 km. 1
- A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10^-4 J by the end of the second revolution aft… Answer: 1. 0.1\ m/s² Key idea: constant tangential acceleration a gives v²=2as along the arc. 1/2mv²=8×10⁻⁴⇒ v²=dfrac2×8×10⁻⁴0.01=0.16 m ² /... 1
- A particle moves so that its position vector is given by r = ω t x + ω t y. Where ω is a constant. Which of the following is true ? Answer: 3. Velocity is perpendicular to r and acceleration is directed towards the origin. Key idea: this is uniform circular motion of unit... 1
- The molecules of a given mass of a gas have r.m.s. velocity of 200\ ms^-1 at 27^° C and 1.0×10^5\ Nm^-2 pressure. When the temperature and pressure of the gas are respectively, 127^° C and 0.05×10^5\ Nm^-2, the r.m.s. velocity of its molecules in ms^… Answer: 2. 400/√(3) Key idea: v_rms∝sqrt T ; it does not depend on pressure directly for a fixed gas. v₂/v₁=√(400/300)=2/sqrt3 , so v₂=400/s... 1
- A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross - section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively, from the axis of the wire is : Answer: 3. 1 Key idea: use Ampere's law. Inside the wire, B=μ₀Ir/2π a² ; outside, B=μ₀I/2π r . At r=a/2 : B=μ₀I/4π a . At r=2a : B'=μ₀I/4π a... 1
- A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be : Answer: 1. 2μ₀ Ii/3π Key idea: forces on the two sides parallel to the wire add up; forces on the other two sides cancel. Side nearest the w... 1
- The magnetic susceptibility is negative for : Answer: 1. diamagnetic material only Key idea: only diamagnetic materials get magnetised opposite to the applied field. Diamagnetic: chi sma... 1
- In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle 30^° when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of : Answer: 4. sin⁻¹(3/4) Key idea: single-slit minima satisfy asinθ=nλ ; secondary maxima are approximately at asinθ=(n+1/2)λ . First minimum a... 1
- The intensity at the maximum in a Young's double slit experiment is I_0. Distance between two slits is d = 5λ, where λ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at… Answer: 4. I₀/2 Key idea: find the phase difference at the point in front of one slit, then use I=I₀cos²(φ/2) . The point is d/2 from the ce... 1