Physics
- Find the torque about the origin when a force of 3j N acts on a particle whose position vector is 2k m. Answer: 3. -6i N m Torque vecτ=vec r×vec F . vecτ=2hat k×3hat j=6(hat k×hat j)=6(-hat i)=-6hat i\ N m Since hat j×hat k=hat i , reversing th... 1
- Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened.… Answer: 2. adiabatic The system is thermally insulated, so no heat enters or leaves: Q=0 . That makes the process adiabatic. (This is a free... 1
- A 800 turn coil of effective area 0.05 m^2 is kept perpendicular to a magnetic field 5×10^-5 T. When the plane of the coil is rotated by 90^° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be : Answer: 4. 0.02 V The coil starts perpendicular to the field (flux =NBA ) and, after rotating 90^° , lies parallel to it (flux zero). ε=Δφ/Δ... 1
- A parallel plate capacitor of capacitance 20 μF is being charged by a voltage source whose potential is changing at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacit… Answer: 2. 60 μ A, 60 μ A In a charging capacitor the conduction current in the wires equals the displacement current between the plates, so... 1
- The correct Boolean operation represented by the circuit diagram drawn is : Answer: 3. NAND In the circuit the two switches A and B are in series between the LED node and ground. Taking the switch position 1 as close... 1
- A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance, d, from the centre of the conductor, is correctly represented by the figure : Answer: 3. [graph] B increasing linearly for d < R, peak at R, then decreasing for d > R By Ampere's law for a cylindrical conductor with un... 1
- The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.y-projection of the radius vector of rotating particle P is : Answer: 4. y(t) = 3cos(π t/2) , where y in m From the figure, A=3 m, T=4 s so ω=2π/T=π/2 rad/s. At t=0 the particle is at the top of the cir... 1
- In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = A^2 B^1/2C^1/3 D^3, will be : Answer: 2. 16% For a product or quotient, the maximum fractional error is the sum of each power times its fractional error. Δ X/X×100=2(1)+1... 1
- In which of the following processes, heat is neither absorbed nor released by a system ? Answer: 2. adiabatic In an adiabatic process Δ Q=0 by definition: no heat enters or leaves the system. In isothermal, isobaric and isochoric... 1
- The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively : Answer: 3. 3.4 eV, -6.8 eV For an electron in a bound orbit, KE=-E and PE=2E . With E=-3.4 eV: KE=+3.4 eV and PE=-6.8 eV. Check: 3.4-6.8=-3.... 1
- α-particle consists of : Answer: 1. 2 protons and 2 neutrons only An α -particle is the nucleus of a helium atom, ⁴₂He : 2 protons and 2 neutrons, with no electrons. 1
- Which of the following acts as a circuit protection device ? Answer: 4. fuse A fuse contains a thin wire that melts when the current exceeds a safe limit, breaking the circuit and protecting the applia... 1
- Six similar bulbs are connected as shown in the figure with a DC source of emf E, and zero internal resistance.The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section… Answer: 2. 9 : 4 From the figure, the three bulbs of section A are in parallel with each other, as are the three bulbs of section B. The two... 1
- In the circuits shown below, the readings of the voltmeters and the ammeters will be : Answer: 3. V₁ = V₂ and i₁ = i₂ Treat the voltmeters as ideal (infinite resistance), so they draw no current. Circuit 1: the 10 Ω resistor is... 1
- An electron is accelerated through a potential difference of 10,000 V. Its de Broglie wavelength is, (nearly) : (m_e = 9×10^-31 kg) Answer: 2. 12.2×10⁻¹² m de Broglie wavelength of an electron accelerated through V : λ=h/√(2meV) . Substituting h=6.63×10⁻³⁴ , m=9×10⁻³¹ , e... 1
- For a p-type semiconductor, which of the following statements is true ? Answer: 2. Holes are the majority carriers and trivalent atoms are the dopants. A p-type semiconductor is made by doping silicon or germaniu... 1
- Two point charges A and B, having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes : Answer: 2. 9F/16 25% of A's charge is 0.25Q . After transfer: q_A=0.75Q and q_B=-Q+0.25Q=-0.75Q . Coulomb force F∝ q_Aq_B at the same distan... 1
- Two parallel infinite line charges with linear charge densities +λ C/m and -λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges ? Answer: 3. λ/πε₀ R N/C The field of an infinite line charge at distance r is E=λ/2πε₀r . Midway, r=R for each line. The + λ line pushes away... 1
- A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre : Answer: 2. zero as r increases for r < R, decreases as r increases for r > R For a uniformly charged hollow sphere, by Gauss's law: Inside (... 1
- A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth ? Answer: 4. 100 N Inside the earth at depth d , g'=g(1-d/R) . Halfway to the centre means d=R/2 , so g'=g/2 . Weight =200/2=100 N. 1
- The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is : Answer: 3. 1/2mgR Work done = change in gravitational potential energy. W=-GMm/R+h+GMm/R . With h=R : W=GMm(1/R-dfrac12R)=GMm/2R . Using GM=... 1
- The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.… Answer: 1. 30^° west To cross along the shortest path (straight north), the swimmer's velocity component along the river flow must cancel th... 1
- Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speed v_A and v_B respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be : Answer: 4. 1 : 1 Angular speed ω=2π/T . Both particles have the same period T , so they have the same angular speed. ω_A:ω_B=1:1 . (Their li... 1
- When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60^° with horizontal, it can travel a distance x_1 along the plane. But when the inclination is decreased to 30^° and the same object is shot with the same veloci… Answer: 3. 1:√(3) On a smooth incline the retardation is gsinθ . For the same launch speed v , the distance up the plane is x=v²/2gsinθ , so... 1