Practice Questions

Q5. Three masses m, 2 m and 3 m are moving in x −y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: (1) 12 u (^i + √3^j) (2) 12u (^i −√3^j) (3) 12 u (−^i + √3^j) (4) 12u (−^i −√3^j)

Q5. A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? (1) 2g (2) g 3 2 (3) 5g (4) g 6

Q5. A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio sinθc sinθs is : (1) 8 (2) 7 √87 (3) (4) 15 14 √1514

Q5. A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 m s−1 . The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 m s−2) JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) 1. 73 kg m2 s−1 (2) 3. 46 kg m2 s−1 (3) 3. 0 kg m2 s−1 (4) 6. 0 kg m2 s−1

Q6. India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M . If the semi-major axis of Earth's orbit is ae = 1.5 × 1011m , that of Mar's orbit JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper am = 2.28 × 1011m, taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth. (1) 220 days. (2) 500 days. (3) 260 days. (4) 320 days.

Q6. A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by ' C '. The angular momentum from the origin O can be written as: JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) va (1 + cos 2θ) (2) va (1 + cos θ) (3) va cos 2θ (4) va

Q6. Match List ‐I (Event) with List ‐ II (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists. List-I List-II (a) The rotation period of earth (i) 105 s (b) Revolution period of earth (ii) 107 s (c) Period of a light wave (iii) 10−15 s (d) Period of a sound wave (iv) 10−3 s (1) (a)‐(i), (b)‐(ii), (c)‐(iii), (d)‐(iv) (2) (a)‐(ii), (b)‐(i), (c)‐(iii), (d)‐(iv) (3) (a)‐(i), (b)‐(ii), (c)‐(iv), (d)‐(iii) (4) (a)‐(ii), (b)‐(i), (c)‐(iv), (d)‐(iii) + N kg−1 . The change in the gravitational potential

Q6. A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension : (1) Angular momentum is conserved (2) Angular momentum changes in magnitude but not in direction (3) Angular momentum changes in direction but not (4) Angular momentum changes both in direction and in magnitude magnitude

Q6. From a sphere of mass M and radius R, a smaller sphere of radius R2 is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is: (1) 41GM2 (2) 41GM2 3600R2 450R2 (3) 59GM2 (4) GM2 450R2 225R2 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q7. The gravitational field in a region is given by →g= (5ˆi 12ˆj) energy of a particle of mass 2 kg when it is taken from the origin to a point (7 m, −3 m) is (1) 71 J (2) 13√58 J (3) 2 J (4) 1 J

Q7. The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of 109Nm−2 . For a given value of pressure, the fractional compression in volume is ΔV . Which of the following statements V about ΔVV for these three liquids is correct ? (1) Ethanol > Water > Mercury (2) Water > Ethanol > Mercury (3) Mercury > Ethanol > Water (4) Ethanol > Mercury > Water

Q7. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is JEE Main 2014 (06 Apr) JEE Main Previous Year Paper (1) √GMR (2) √2√2 GMR + + R (1 R (1 2√2) (3) √GM (4) 1 2√2) 2 √GM

Q7. In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is : (1) Young's modulii < shear modulii < bulk modulii (2) Bulk modulii < shear modulii < Young's modulii (3) Shear modulii < Young's modulii < bulk modulii (4) Bulk modulii < Young's modulii < shear modulii

Q7. Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ' d '? (Speed of m1 is v1 and that of m2 is v2 ) (1) (2) v1 = v2 2G v1 = m2√ d (m1 + m2 ) 2G v2 = m1√ d (m1 + m2 ) (3) (4) 2G v1 = v1 = m1√ d (m1 + m2 ) m2√2Gm1 2G v2 = v2 = m2√ d (m1 + m2 ) m2√2Gm2

Q8. The velocity of water in a river is 18 km h−1 near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = 10−2 poise. (1) 10−4 N m−2 (2) 10−3 N m−2 (3) 10−2 N m−2 (4) 10−1 N m−2

Q8. Steel ruptures when a shear of 3.5 × 108 N m−2 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly: (1) 1.4 × 104 N (2) 2.7 × 104 N (3) 3.3 × 104 N (4) 1.1 × 104 N

Q8. There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are filled in the tube. Each liquid subtends 90o angle at centre. Radius joining their interface makes an angle α with vertical. Ratio d1 is : d2 (1) 1+sinα (2) 1+cosα 1−sinα 1−cosα (3) 1+tanα (4) 1+sinα 1−tanα 1−cosα

Q8. A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio xy is : (1) ( RR +− dd ) (2) ( RR +− dd ) (3) (1 −2dR ) (4) (1 −dR )

Q8. The average mass of rain drops is 3.0 × 10−5 kg and their avarage terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year. (1) 3.5 × 105 J (2) 4.05 × 104 J (3) 3.0 × 105 J (4) 9.0 × 104 J

Q9. A large number of liquid drops each of radius r coalesce to form a single drop of the radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid T , density ρ ) ( 1r −1R ) (1) √2Tρ ( 1r −1R ) (2) √6Tρ ( 1r −1R ) (3) √4Tρ ( 1r −1R ) (4) √Tρ

Q9. Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27oC to 77oC ? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible). (1) 8 min 20 s (2) 7 min (3) 14 min (4) 6 min 2 s

Q9. A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8 ). The height of water is 3 m and that of kerosene 2 m. When the hole is opened the velocity of fluid coming out from it is nearly: (take g = 10 ms−2 and density of water = 103 kg m−3) (1) 10.7 ms−1 (2) 9.6 ms−1 (3) 8.5 ms−1 (4) 7.6 ms−1

Q9. A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius ' a '. The time in which it will be emptied is: (1) 2 A (2) √2 A πa2 √hg πa2 √hg (3) 2√2 A (4) A g πa2 √h g √2πa2 √h

Q9. On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is : (density of water is ρw ) (1) R2√2ρw3T g ​ (2) R2√ρw6Tg (3) R2√ρwT g (4) R2√3ρwT g

Q10. In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm2 and 10 mm2 respectively. The rate at which water flows through the tube is (g = 10 m s−2) JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) 7. 5 cc s−1 (2) 12. 5 cc s−1 (3) 8. 0 cc s−1 (4) 10. 0 cc s−1