Practice Questions

Q4. A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is: (1) 2 Mg (2) 2 Mg 2m+M 2M+m (3) 2 mg (4) 2 mg 2M+m 2m+M

Q4. A body of mass 𝑚= 10−2 kg is moving in a medium and experiences a frictional force 𝐹= −𝑘𝑣2 . Its initial 1 speed is 𝑣0 = 10 m s−1 . After 10 s its kinetic energy is 8𝑚𝑣02, then value of 𝑘 will be:- (1) 10−1 kg m-1 s-1 (2) 10−3 kg m-1 (3) 10−3 kg 𝑠-1 (4) 10−4 kg m-1

Q5. The moment of inertia of a uniform cylinder of length 𝑙 and radius 𝑅 about its perpendicular bisector is 𝐼. What is the ratio 𝑙/ 𝑅 such that the moment of inertia is minimum? JEE Main 2017 (02 Apr) JEE Main Previous Year Paper 3 3 (1) (2) √2 √ 2 (3) √3 (4) 1 2

Q5. Two particles A and B of equal mass M are moving with the same speed v as shown in figure. They collide completely inelastic and move as a single particle C . The angle θ that the path of C makes with the X -axis is JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper given by- (1) tan θ = √3− √2 (2) tan θ = 1− √2 1− √2 √2 (1+ √3) (3) tan θ = 1− √3 (4) tan θ = √3+ √2 1+ √2 1− √2

Q5. Moment of inertia of an equilateral triangular lamina ABC , about the axis passing through its centre O and perpendicular to its plane is I0 as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper is: (1) 7 8 I0 (2) 1516 I0 (3) 4 3 I0 (4) 31I032

Q6. A slender uniform rod of mass 𝑀 and length 𝑙 is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle 𝜃 with the vertical is: (1) 2𝑔 (2) 3𝑔 3𝑙cos⁡𝜃 2𝑙sin𝜃 (3) 2𝑔 (4) 3𝑔 3𝑙sin⁡𝜃 2𝑙cos⁡𝜃

Q6. In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct? (1) Every object that is weighed using this balance (2) Left arm is shorter than the right arm appears lighter than its actual weight (3) Both the arms are of same length (4) Left arm is longer than the right arm

Q6. A circular hole of radius R is made in a thin uniform disc having mass and radius R, as shown in figure. The 4 moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is- (1) 219MR2 (2) 237MR2 256 512 (3) 197MR2 (4) 19MR2 256 512

Q7. The mass density of a spherical body is given by ρ(r) = kr for r ≤R and ρ(r) = 0 for r > R, where r is the distance from the center. The correct graph that describes qualitatively the acceleration, a of a test particle as a function of r is: JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q7. The variation of acceleration due to gravity 𝑔 with distance 𝑑 from the centre of the earth is best represented by (𝑅= Earth's radius): (1) (2) (3) (4)

Q7. If the Earth has no rotational motion, the weight of a person on the equator is W . Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3 W . The radius 4 of the Earth is 6400 km and g = 10 m s−2 (1) 0.63 × 10−3 rad s−1 (2) 0.28 × 10−3 rad s−1 (3) 1.1 × 10−3 rad s−1 (4) 0.83 × 10−3 rad s−1

Q8. A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density remains same, the stress in the leg will change by a factor of: 1 (1) (2) 9 81 (3) 1 (4) 81 9

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

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

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

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. 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

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

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.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)

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.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

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