Practice Questions

Q1. In the following I refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity: (1) M−1L−3T3I (2) M−1L−3T3I2 (3) M−1L3T3I (4) ML−3T−3I2

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 point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals μ . The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction μ and the distance x = (QR) , are respectively close to: (1) 0.29 and 3.5 m (2) 0.29 and 6.5 m (3) 0.2 and 6.5 m (4) 0.2 and 3.5 m

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. 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

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

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. A particle of mass m is moving along the side of a square of side 'a', with a uniform speed υ in the x-y plane as shown in the figure: → Which of the following statements is false for the angular momentum L about the origin? JEE Main 2016 (03 Apr) JEE Main Previous Year Paper → → mυ (1) R (2) L = + L = Rˆk a]ˆk mυ[ √2 √2 when the particle is moving from B to C. when the particle is moving from D to A. → → R (3) (4) L = −mυ + a]ˆk √2 Rˆk L = mυ[ √2 when the particle is moving from A to B. when the particle is moving from C to D.

Q5. The velocity-time graph of a particle of mass 10 kg is shown in the figure. The net work done on the particle in the first two seconds of the motion is (1) −9300 J (2) 12000 J (3) −4500 J (4) −12000 J

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

Q5. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to: (1) go straight. (2) turn left and right alternately. (3) turn left. (4) turn right.

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. 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 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. A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal: (1) L(1 + 29 πYR2Mg ) (2) L(1 + 19 πYR2Mg ) (3) L(1 + 13 πYR2Mg ) (4) L(1 + 23 πYR2Mg )

Q7. A pendulum clock loses 12 s a day if the temperature is 40o C and gains 4s a day if the temperature is 20o C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively: (1) 30oC; α = 1.85 × 10−3 / oC (2) 55oC; α = 1.85 × 10−2 / oC (3) 25oC; α = 1.85 × 10−5 / oC (4) 60oC; α = 1.85 × 10−4 / oC

Q8. An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth's surface. The radius of the earth is R, while its mass is M . The gravitational pull FG on the astronaut is (1) Zero since astronaut feels weightless (2) GMm < FG < GMmR2 (R+h)2 (3) FG = GMm (4) 0 < FG < GMmR2 (R+h)2

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

Q8. Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then: (1) 1 (2) x = r( H+hH ) x = r( H+hH ) 4 1 H ) 2 (3) x = r( H+hH ) 2 (4) x = r( H+h

Q9. A bottle has an opening of radius a and length b . A cork of length b and radius (a + Δa) where (Δa ≪a), is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is B and the coefficient of friction between the bottle and cork is μ , then the force needed to push the cork into the bottle is (1) (πμBb)a (2) (2πμBb) Δ a (3) (πμBb) Δ a (4) (4πμBb) Δ a

Q9. An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn = constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) : (1) n = CP−C (2) n = C−CV C−CV C−CP (3) n = CP (4) n = C−CP CV C−CV

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.The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is (1) 2 (2) 3 5 2 (3) 3 (4) 2 5 3 Q11. 200 g water is heated from 40 oC to 60 oC . Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J kg−1 K−1 ): (1) 167.4 kJ (2) 8.4 kJ (3) 4.2 kJ (4) 16.7 kJ

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

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