Practice Questions

Q1. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be: (1) 92 ± 1.8 s (2) 92 ± 3 s (3) 92 ± 2 s (4) 92 ± 5.0 s

Q2. A, B, C , and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity? (1) BD C −A2D2C (2) A2 −B2C 2 (3) A −C (4) A2−AC B D

Q2. A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle θ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction μmin between the mass and the inclined surface such that the mass does not move is: (1) tan 2θ (2) tan θ (3) 3 tan θ (4) 2 tan θ

Q3. Which of the following option correctly describes the variation of the speed υ and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force F = −kυ , where 'k' is a constant, on the body? (Graphs are schematic and not drown to scale) (1) (2) (3) (4)

Q3. A particle of mass m is acted upon by a force F given by the empirical law F = R v(t). If this law is to be t2 tested experimentally by observing the motion starting from rest, the best way is to plot (1) log v(t) against 1t (2) v(t) against t2 (3) log v(t) against 1 (4) log v(t) against t t2

Q3. A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8 × 107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms−2 : (1) 9.89 × 10−3 kg (2) 12.89 × 10−3 kg (3) 2.45 × 10−3 kg (4) 6.45 × 10−3 kg

Q4. A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force W on the car. While moving uphill on the road at a speed of 10 ms−1 , the car needs power P. If 20 it needs power P while moving downhill at speed υ then value of υ is: 2 (1) 20 ms−1 (2) 5 ms−1 (3) 15 ms−1 (4) 10 ms−1

Q4. Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to : (Take the radius of the drum to be 1.25 m and its axle to be horizontal) : (1) 27.0 (2) 0.4 (3) 1.3 (4) 8.0

Q5. A cubical block of side 30 cm is moving with velocity 2 m s−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is : JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper (1) 13.3 (2) 5.0 (3) 9.4 (4) 6.7

Q6. The figure shows an elliptical path ABCD of a planet around the sun S such that the area of triangle CSA is 1 4 the area of the ellipse. (see figure) with DB as the major axis, and CA as the minor axis. If t1 is the time taken for the planet to go over path ABC and t2 for path taken over CDA then: (1) t1 = 4t2 (2) t1 = 2t2 (3) t1 = 3t2 (4) t1 = t2

Q6. A satellite is revolving in a circular orbit at a height h from the earth's surface (radius of earth R; h<<R ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to (Neglect the effect of atmosphere.) (1) √gR2 (2) √gR (√2 −1) (3) √2 gR (4) √ gR

Q6. A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2Rt2 , where n is a constant. The power delivered to the particle by the force acting on it, is : (1) 1 Mn2R2t2 (2) Mn2R2t 2 (3) MnR2t2 (4) MnR2t JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q7. In the figure shown ABC is a uniform wire. If the center of mass of the wire lies vertically below point A, then BC is close to AB (1) 1. 85 (2) 1. 5 (3) 1. 37 (4) 3

Q8. n moles of an ideal gas undergoes a process A →B as shown in the figure. The maximum temperature of the gas during the process will be: JEE Main 2016 (03 Apr) JEE Main Previous Year Paper (1) 9 P0V0 (2) 9 P0V0 2nR nR (3) 9 P0V0 (4) 3 P0V0 4nR 2nR

Q9. A simple pendulum made of a bob of mass m and a metallic wire of a negligible mass has a time period of 2 s at T = 0°C. If the temperature of the wire is increased, and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S . If the coefficient of linear expansion of metal is α , then the value of S is (1) α (2) 2α 2 (3) α (4) 1 α

Q10.A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance 2A from equilibrium position. The new amplitude of the motion is: 3 (1) A√3 (2) 7A3 (3) A 3 √41 (4) 3A

Q10.A Carnot freezer takes heat from water at 0oC inside it and rejects it to the room at a temperature of 27oC. The latent heat of ice is 336 × 103 Jkg−1. If 5kg of water at 0oC is converted into ice at 0oC by the freezer, then the energy consumed by the freezer is close to : (1) 1 .51 ×105 J (2) 1 .68 ×106 J (3) 1 .71 ×107 J (4) 1 .67 ×105 J

Q11.A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now: (1) 2f (2) f (3) f (4) 3f 2 4

Q12.In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to : (1) 0.7 Hz (2) 1.9 Hz (3) 1.2 Hz (4) 0.1 Hz

Q13.Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. one of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. speed of sound is 330 m/sec: (1) 450 Hz (2) 540 Hz (3) 270 Hz (4) 648 Hz

Q13.A toy-car, blowing its horn, is moving with a steady speed of 5 m s−1 , away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m s−1 the frequency of the horn of the toy car is close to (1) 680 Hz (2) 510 Hz (3) 340 Hz (4) 170 Hz

Q14.The potential (in volts) of a charge distribution is given by V(z) = 30 −5z2 for |z| ≤1 m V(z) = 35 −10 |z| for |z| ≥1 m . V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume ρ0 (in units of ϵ0 ) which is spread over a certain region, then choose the correct statement. (1) ρ0 = 20 ϵ0 in the entire region (2) ρ0 = 10 ϵ0 for |z| ≤1 m and ρ0 = 0 else where (3) ρ0 = 20 ϵ0 for |z| ≤1 m and ρ0 = 0 else where (4) ρ0 = 40 ϵ0 in the entire region JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q14.A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 μF and 9 μF capacitors), at a point distant 30 m from it, would equal: (1) 420 N/C (2) 480 N/C (3) 240 N/C (4) 360 N/C

Q15.Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 μF is : (1) 32 μF (2) 31 μF 23 23 (3) 33 μF (4) 34 μF 23 23

Q16.Hysteresis loops for two magnetic materials A and B are given below: These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use: (1) A for transformers and B (2) B for electromagnets and transformers. for electric generators. (3) A for electric generators and transformers. (4) A for electromagnets and B for electric generators.