Practice Questions

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.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

Q10.An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (Take Cv = 1.5R, where R is gas constant) (1) 0. 24 (2) 0. 15 (3) 0. 32 (4) 0. 08

Q11.An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp) and at constant volume (CV) is: (1) 7 (2) 6 5 (3) 7 (4) 5 2 2

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.A block of mass 0. 1 kg is connected to an elastic spring of spring constant 640 N m−1 and oscillates in a damping medium of damping constant 10−2 kg s−1 . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to- (1) 2 s (2) 5 s (3) 3 s (4) 7 s

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.A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, y(x, t) = 0.5 sin( 5π4 x) cos(200πt). What is the speed of the travelling wave moving in the positive x direction? ( x and t are in meter and second, respectively) (1) 120 m s−1 (2) 90 m s−1 (3) 160 m s−1 (4) 180 m s−1 JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper

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

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

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

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

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

Q17. A 9 V battery with an internal resistance of 0.5 Ω is connected across an infinite network, as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal. Choose the correct statement. (1) Reading of A1 is 18 A . (2) Reading of V is 9 V . (3) Reading of V is 7 V . (4) Reading of A1 is 2 A .

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

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

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.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