Practice Questions

Q8. A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by ΔT . The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young's modulus, and α its coefficient of linear expansion. Then, F is equal to: (1) lAY α ΔT (2) A Yα ΔT (3) AY (4) l2 Yα ΔT αΔT

Q8. Two tubes of radii r1 and r2 and lengths l1 and l2, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes. If P2 is 4P1 and l2 is l14 then the radius r2 will be equal to : (1) 4r1 (2) r1 (3) 2r1 (4) r12

Q9. In an experiment, a sphere of aluminium of mass 0. 20 kg is heated up to 150°C . Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0. 025 kg . The final temperature of the system is 40oC . The specific heat of the aluminium is(take 4. 2 Joule = 1 calorie ) (1) 434 J kg−1 oC (2) 378 J kg−1°C (3) 315 J kg−1 oC (4) 476 J kg−1 oC

Q9. A copper ball of mass 100 g is at a temperature 𝑇. It is dropped in a copper calorimeter of mass 100 g, filled with 170 g of water at room temperature. Subsequently, the temperature of the system is found to be 75°C. 𝑇 is given by: (Given: room temperature = 30°C, specific heat of copper = 0.1 cal g-1 °C-1) (1) 825°C (2) 800°C (3) 885°C (4) 1250°C JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q9. A steel rail of length 5 m and area of cross section 40 cm2 is prevented from expanding along its length while the temperature rises by 10°C . If coefficient of linear expansion and Young's modulus of steel are 1.2 × 10−5 K−1 and 2 × 1011 N m−2 respectively, the force developed in the rail is approximately: (1) 2 × 107 N (2) 2 × 109 N (3) 3 × 10−5 N (4) 1 × 105 N

Q10.For the P −V diagram given for an ideal gas Out of the following which one correctly represents the T −P diagram? JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q10.An external pressure 𝑃 is applied on a cube at 0°C so that it is equally compressed from all sides. 𝐾 is the bulk modulus of the material of the cube and 𝛼 is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by: 𝑃 (1) 3𝑃𝐾𝛼 (2) 3𝛼𝐾 (3) 𝑃 (4) 3𝛼 𝛼𝐾 𝑃𝐾 𝑅 Q11.𝐶𝑝- 𝐶𝑣= 𝑀 and 𝐶𝑣 are specific heats at constant pressure and constant volume respectively. It is observed that, 𝐶𝑝- 𝐶𝑣= 𝑎 for hydrogen gas and 𝐶𝑝- 𝐶𝑣= 𝑏 for nitrogen gas. The correct relation between 𝑎 and 𝑏 is: (1) 𝑎= 28 𝑏 (2) 𝑎= 1 𝑏 14 (3) 𝑎= 𝑏 (4) 𝑎= 14𝑏

Q11. N moles of diatomic gas in a cylinder is at a temperature T . Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas is (1) 0 (2) 25 nRT (3) 3 nRT (4) 1 nRT 2 2

Q12.The temperature of an open room of volume 30 m3 increases from 17°C to 27°C due to the sunshine. The atmospheric pressure in the room remains 1 × 105 Pa. If 𝑛𝑖 and 𝑛𝑓 are the number of molecules in the room before and after heating, then 𝑛𝑓- 𝑛𝑖 will be: (1) -2.5 × 1025 (2) -1.61 × 1023 (3) 1.38 × 1023 (4) 2.5 × 1025

Q12.The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1. At, t = 0 the displacement is 5 m. What is the maximum acceleration? The initial phase is π4 . (1) 500 m s−2 (2) 750√2 m s−2 (3) 750 m s−2 (4) 500√2 m s−2

Q13.A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is (1) 2 Hz (2) 14 Hz (3) 1 Hz (4) 12 Hz 2√2

Q13.A particle is executing simple harmonic motion with a time period 𝑇. At time 𝑡= 0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like: (1) (2) (3) (4)

Q13.In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5 × 10−4 s, the difference in radii, |r1 −r2| is best-given by (1) 0. 01 cm (2) 0. 05 cm (3) 0. 5 cm (4) 1 cm

Q14.Two wires W1 and W2 have the same radius r and respective, densities ρ1 and ρ2 , such that ρ2 = 4ρ1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T . The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is (1) 4 : 1 (2) 1 : 2 (3) 1 : 1 (4) 1 : 3

Q14.An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 × 108 m s-1) (1) 15 . 3 GHz (2) 10 . 1 GHz (3) 12 . 1 GHz (4) 17 . 3 GHz

Q15.There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P , in the region, is found to vary between the limits 589. 0 V to 589. 8 V . What is the potential at a point on the JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper sphere whose radius vector makes an angle of 60° with the direction of the field? (1) 589. 4 V (2) 589. 5 V (3) 589. 2 V (4) 589. 6 V

Q15.An electric dipole has fixed dipole moment →𝑝, which makes angle 𝜃 with respect to 𝑥- axis. When subjected to an electric field →𝐸1 = 𝐸^𝑖, it experiences a torque →𝑇1 = 𝜏^𝑘. When subjected to another electric field →𝐸2 = √3 𝐸1^𝑗 it experiences a torque →𝑇2 = - →𝑇1 . The angle 𝜃 is: (1) 90𝑜 (2) 30𝑜 (3) 45𝑜 (4) 60𝑜

Q16.A capacitance of 2 μF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 𝜇F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is: (1) 32 (2) 2 (3) 16 (4) 24 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q16.The energy stored in the electric field produced by a metal sphere is 4. 5 J. If the sphere contains 4 μC charge, its radius will be: [Take : 4π∈01 = 9 × 109 N m2 C−2] (1) 32 mm (2) 16 mm (3) 28 mm (4) 20 mm

Q16.A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is: (1) Away from the wire (2) Towards the wire (3) Parallel to the wire along the current (4) Parallel to the wire opposite to the current

Q17.In the given circuit diagram, when the current reaches a steady-state in the circuit, the charge on the capacitor of capacitance 𝐶 will be: (1) 𝐶𝐸 𝑟1 (2) 𝐶𝐸 𝑟1 + 𝑟 𝑟1 𝑟2 (3) 𝐶𝐸 (4) 𝐶𝐸 𝑟2 + 𝑟 𝑟+ 𝑟2

Q17.A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2. 4 mm. Find the dielectric constant of the slab. (1) 6 (2) 4 (3) 3 (4) 5

Q18.A potentiometer PQ is set up to compare two resistances, as shown in the figure. The ammeter A in the circuit reads 1. 0 A when the two-way key K3 is open. The balance point is at a length l1 cm from P when the two- way key K3 is plugged in between 2 and 1 , while the balance point is at a length l2 cm from P when the key K3 is plugged in between 3 and 1 . The ratio of two resistances R1R2 , is found to be (1) l1 (2) l2 l1−l2 l2−l1 (3) l1 (4) l1 l1+l2 l2−l1

Q18. In the above circuit the current in each resistance is: (1) 0 A (2) 1 A (3) 0 . 25 A (4) 0 . 5 A

Q18.In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P = 4 Ω and the neutral point N is at 60 cm from A . Now an unknown resistance R is connected in series to P and the new JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper position of the neutral point is at 80 cm from A . The value of unknown resistance R is - (1) 33 5 Ω (2) 6 Ω (3) 20 3 Ω (4) 7 Ω