Practice Questions

Q7. The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be: (1) √3 2 s (2) √32 s (3) 3 s (4) 2√3 s 2

Q7. A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is: (1) F (2) 3F 3 mR 2 m R (3) 2F (4) F 3 m R 2 m R

Q7. An 𝐿 -shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If 𝐴𝐵= 𝐵𝐶, and the angle made by 𝐴𝐵 with downward vertical is 𝜃, then: 2 1 (1) tan⁡𝜃= (2) tan⁡𝜃= √3 3 (3) tan⁡𝜃= 1 (4) tan⁡𝜃= 1 2 2√3

Q8. n moles of an ideal gas with constant volume heat capacity Cv undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is: (1) 4nR (2) 4nR Cv+nR Cv−nR (3) nR (4) nR Cv+nR Cv−nR

Q8. A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms-1 . Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to: (1) 106N m-2 (2) 104N m-2 (3) 108N m-2 (4) 103N m-2

Q8. A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights ℎ𝑠𝑝ℎ and ℎ𝑐𝑦𝑙 on the inline. The ratio JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper ℎ𝑠𝑝ℎ is given by: ℎ𝑐𝑦𝑙 2 4 (1) (2) √5 5 (3) 14 (4) 1 15

Q8. A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance 3a from the centre will be: (1) GM (2) GM 9a2 3a2 (3) 2GM (4) 2GM 3a2 9a2

Q8. At 40°C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m . The value of M is close to: (Coefficient of linear expansion and Young’s modulus of brass are 10-5 /° C and 1011 N / m2, respectively; g = 10 m s-2 ) (1) 0.9 kg (2) 0.5 kg (3) 1.5 kg (4) 9 kg

Q8. A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2, when falling through the same fluid, the ratio ( v1v2 ) equals: (1) 1 (2) 27 9 (3) 1 (4) 9 27

Q8. The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m3 water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to: (1) 2.9 m (2) 4.8 m (3) 6.0 m (4) 9.6 m

Q8. A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given: Mass of planet = 8 × 1022 kg , Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10-11 Nm2 / kg2 ] (1) 17 (2) 9 (3) 13 (4) 11

Q8. A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be: (1) 1 ρv2 (2) 3 ρv2 4 4 (3) 1 ρv2 (4) ρv2 2

Q8. A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and that of the outer cylinder is K2 . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is: (1) 2K1+3K2 (2) K1+K2 5 2 (3) K1 + K2 (4) K1+3K24

Q9. A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y . When this rod is heated by temperature T and simultaneously subjected to a net longutudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to: (1) F/(3πr2Y T) (2) 9F/(πr2Y T) (3) 6F/(πr2Y T) (4) 3F/ (πr2Y T) Q10. 1 kg of water, at 20 °C is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 Ω. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully is close to [ Specific heat of water = 4200 J kg−1 °C−1 Latent heat of water = 2260 kJ kg−1 ] (1) 3 min (2) 16 min (3) 22 min (4) 10 min

Q9. A heavy ball of mass 𝑀 is suspended from the ceiling of a car by a light string of mass 𝑚 𝑚≪𝑀. When the car is at rest, the speed of transverse waves in the string is 60 ms-1 . When the car has acceleration 𝑎, the wave- speed increases to 60.5 ms-1 . The value of 𝑎, in terms of gravitational acceleration 𝑔, is closed to 𝑔 𝑔 (1) (2) 10 20 (3) 𝑔 (4) 𝑔 5 30

Q9. Water flows into a large tank with flat bottom at the rate of 10−4 m3s−1. Water is also leaking out of a hole of area 1 cm2 at its bottom. If the height of the water in the tank remains steady then this height is: (1) 5.1 cm (2) 1.7 cm (3) 2.9 cm (4) 4 cm

Q9. When 𝑀1 gram of ice at -10oC (specific heat = 0.5 cal g-1 ℃-1 ) is added to 𝑀2 gram of water at 50 oC, finally no ice is left and the water is at 0 oC . The value of latent heat of ice, in cal g-1 is: (1) 50𝑀2 (2) 5𝑀1 - 50 𝑀1 𝑀2 5𝑀2 50𝑀2 (3) - 5 (4) - 5 𝑀1 𝑀1

Q9. Two carnot engines A and B are operated in series. The first one, A, receives heat at T1(= 600K) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at T3(= 400K). Calculate the temperature T2 if the work outputs of the two engines are equal: (1) 500 K (2) 400 K (3) 300 K (4) 600 K

Q9. A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0/3 when in contact with ice. What is the temperature of an object in ∘C , if this thermometer in the contact with the object reads x0/2? (1) 25 (2) 60 (3) 40 (4) 35

Q9. Two satellites, A and B , have masses m and 2m respectively. A is in a circular orbit of radius R and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, KA is: KB (1) 2 (2) 21 (3) 1 (4) √12

Q9. A wooden block floating in a bucket of water has 4 of its volume submerged. When certain amount of an oil is 5 poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is: (1) 0.8 (2) 0.7 (3) 0.5 (4) 0.6

Q9. A rocket has to be launched from earth in such a way that it never returns. If 𝐸 is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon. E E (1) (2) 64 4 (3) E (4) E 32 16

Q10.A rod, of length 𝐿 at room temperature and uniform area of cross section 𝐴, is made of a metal having coefficient of linear expansion 𝛼 / °𝐶 It is observed that an external compressive force 𝐹 is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by ∆𝑇 K Young's modulus, 𝑌 for this metal is: 𝐹 2𝐹 (1) (2) 𝐴𝛼∆𝑇- 273 𝐴𝛼∆𝑇 𝐹 𝐹 (3) (4) 𝐴𝛼∆𝑇 2𝐴 𝛼∆𝑇 JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper

Q10.A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is: (1) 3 (2) 2 5 5 (3) 2 (4) 5 3 3

Q10.In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is increased by ΔT . The amount of heat absorbed by gas is (R is gas constant): (1) 1 2 RΔT (2) 21 KRΔT (3) 2 3 RΔT (4) 2 3K ΔT