Physics
- A container has two chambers of volumes V_1 = 2 litres and V_2 = 3 litres separated by a partition made of a thermal insulator. The chambers contains n_1 = 5 and n_2 = 4 moles of ideal gas at pressures p_1 = 1 atm and p_2 = 2 atm, respectively. When… Answer: 2. 1.6 atm Key idea: no heat or work leaves the container, so the total internal energy is conserved. For the same gas, this gives n... 1
- An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster's angle. Then- Answer: 1. reflected light is completely polarized and the angle of reflection is close to 60^° Key idea: at Brewster's angle tan i_B=μ , an... 1
- In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency ω(t) and average amplitude A(t) of the system change with time t.… Answer: 2. Graph pair: ω(t) rises and saturates; A(t) decays Key idea: the frequency of a spring-mass system is ω=√(k/m) , and sand leaking... 1
- Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature… Answer: 3. 5/3 Key idea: in steady state the same heat current flows through all three rods, so kA Δ T/l is equal for each. With equal A and... 1
- A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density ρ and takes a spherical shape of radius R. When the gas is allowed to flow freely out… Answer: 3. a=-1/2,α=-1/2,β=-1,γ=1/2,δ=7/2 Key idea: the excess pressure inside the balloon is proportional to S/r (it is 4S/r in the standar... 1
- The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density. Answer: 4. 108 days Key idea: no external torque, so angular momentum L=Iω is conserved. For a uniform sphere, I=2/5MR² . Mass stays the sam... 1
- A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of 60^° with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take g = 10 m/s^2) Answer: 2. 100√(3) N Key idea: the wall is smooth, so the wall force N is horizontal. For equilibrium, floor friction f equals N , and torqu... 1
- A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is : Answer: 3. 7/57 Key idea: moment of inertia of the remaining part = full sphere - removed sphere, using the parallel-axis theorem for the cu... 1
- The current passing through the battery in the given circuit, is: Answer: 2. 0.5 A Key idea: the middle network is a balanced Wheatstone bridge, so the 6\ Ω resistor carries no current. Points C and D are j... 1
- AB is a part of an electrical circuit (see figure). The potential difference "V_A - V_B", at the instant when current i = 2 A and is increasing at a rate of 1 amp / second is: Answer: 4. 10 volt Key idea: going from A to B, add the potential change across each element. The current flows from A to B and is increasin... 1
- The electric field in a plane electromagnetic wave is given by E_z = 60(5x + 1.5×10^9 t) V/m. Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) : Answer: 1. B_y = 2×10⁻⁷cos(5x+1.5×10⁹ t)T Key idea: in an EM wave, B₀=E₀/c , and vec E×vec B points along the direction of propagation. The... 1
- The output (Y) of the given logic implementation is similar to the output of an/a ________ gate. Answer: 4. NOR Key idea: write the output of each gate in Boolean form and simplify. The upper gate is a NOR gate with inputs A and B: A+B .... 1
- A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s^2) Answer: 1. 21 NS Key idea: impulse equals change in momentum, and the velocity direction reverses at the ground. v_before=√(2gh₁)=√(2×9.8×40... 1
- There are two inclined surfaces of equal length (L) and same angle of inclination 45^° with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smo… Answer: 4. 0.75 Key idea: for a fixed length L starting from rest, L=1/2 a t² , so t∝ 1/sqrt a . Smooth plane: a_s=gsin45^° . Rough plane: a... 1
- A 2 amp current is flowing through two different small circular copper coils having radii ratio 1:2. The ratio of their respective magnetic moments will be Answer: 1. 1:4 Key idea: the magnetic moment of a current loop is M=IA=Iπ r² . The current is the same (2 A), so M∝ r² : M₁/M₂=(r₁/r₂)²=(1/2... 1
- An electron (mass 9×10^-31 kg and charge 1.6×10^-19C) moving with speed c/100 (c = speed of light) is injected into a magnetic field B of magnitude 9×10^-4 T perpendicular to its direction of motion. We wish to apply an uniform electric field E toget… Answer: 2. vec E is perpendicular to vec B and its magnitude is 27×10² V m ⁻¹ Key idea: for the electron to go undeflected, the electric for... 1
- In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power (p) and magnification (m) for each lens will be, respectiv… Answer: 3. 4p and m⁴ Key idea: powers of thin lenses in contact add, while magnifications of successive images multiply. Power: P=p+p+p+p=4p... 1
- A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is Answer: 2. 125 Key idea: for a compound microscope, the magnification is the product of the objective magnification and the eyepiece magnifi... 1
- Consider a water tank shown in the figure. It has one wall at x = L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes angle θ_0(θ_0 1) with the x-axis at x = L.… Answer: 2. d²y/dx²=ρ g/Sy Key idea: the surface tension pulls the curved surface so that, for each small piece, the net vertical force balan... 1
- The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m. If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the… Answer: 2. 2/3 Key idea: by the work-energy theorem, the brake force does work equal to the kinetic energy lost: F d = K . F_A=100/1000=0.1\... 1
- A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v_0 as shown in figure. If the string gets slack at some point P making an angle θ from the horizontal, the ratio of the speed v of the bob at po… Answer: 4. (sinθ/2+3sinθ)^(1/2) Key idea: the string goes slack when the tension becomes zero, and energy is conserved along the way. At P (... 1
- Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is: Answer: 3. 2 : 9 Key idea: P=V²/R , so R∝1/P at fixed voltage. Take R_A=2 units (1 kW) and R_B=1 unit (2 kW). Series: R_s=3 , so P_s=V²/3 .... 1
- Choose the correct circuit which can achieve the bridge balance. Answer: 2. circuit (2) Key idea: A Wheatstone bridge is balanced when no current flows through G, i.e. P/Q=R/S . The top arms are 10 Ω and 1... 1
- A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to :A. hold the sheet there if it is magnetic.B. hold the sheet there if it is non-magnetic.C. move the sheet away from the pole with uniform velocity if… Answer: 3. A and C only Key idea: A force is needed only if the magnetic pole exerts a force on the sheet. A: A magnetic sheet is attracted... 1