Practice Questions

Q3. An automobile, traveling at 40 km h−1 , can be stopped at a distance of 40 m by applying brakes. If the same automobile is traveling at 80 km h−1 , the minimum stopping distance in metres is (Assume no skidding): (1) 150 m (2) 100 m (3) 75 m (4) 160 m

Q3. A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of 30∘ . The external force required to take the same body up the plane with the same acceleration will be: (g = 10 m/s2) (1) 4 N (2) 14 N (3) 6 N (4) 20 N

Q4. A given object takes n times more time to slide down a 45∘ rough inclined plane as it takes to slide down a perfectly smooth 45∘ incline. The coefficient of kinetic friction between the object and the incline is : 1 (1) 1 (2) 1 − − n2 n2 √1 (3) 1 (4) 1 2−n2 1−n2 √

Q4. A given object takes n times more time to slide down a 45o rough inclined plane as it takes to slide down a perfectly smooth 45o incline. The coefficient of kinetic friction between the object and the incline is: 1 1 (2) 1 − − n2 n2 (1) √1 (3) 1 (4) 1 2−n2 √ 1−n2

Q4. A particle is moving in a circular path of radius a under the action of an attractive potential U = −k . Its total 2r2 energy is: (1) −32 a2k (2) – 4a2k (3) k (4) Zero 2a2

Q4. As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is, 20 cm then under similar conditions as above, the displacement will be: (1) 1.00 cm (2) 0.25 cm (3) 0.37 cm (4) 0.75 cm

Q4. Two particles of the same mass m are moving in circular orbits because of force, given by F (r) = −16r −r3 . The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to (1) 3 × 10−3 (2) 6 × 102 (3) 6 × 10−2 (4) 10−2

Q5. In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is (1) v0 (2) v0 √2 4 (3) √ 2 v0 (4) v02 JEE Main 2018 (08 Apr) JEE Main Previous Year Paper

Q5. A uniform rod AB is suspended from a point X , at a variable distance x from A , as shown. To make the rod horizontal, a mass m is suspended from its end A . A set of (m, x) value is recorded. The appropriate variables JEE Main 2018 (15 Apr) JEE Main Previous Year Paper that give a straight line, when plotted, are: (1) m, x2 (2) m, 1 x2 (3) m, x1 (4) m, x

Q5. A uniform rod AB is suspended from a point X , at a variable distance from x from A , as shown. To make the rod horizontal, a mass m is suspended from its end A . A set of (m, x) values is recorded. The appropriate variable that give a straight line, when plotted, are: (1) m, x1 (2) m, x21 (3) m, x (4) m, x2 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q5. A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z′ axes will be: (1) 1 : 4 (2) 1 : 5 (3) 1 : 3 (4) 1 : 2

Q5. A disc rotates about its axis of symmetry in a hoizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is (g = 10 m/s2) (1) 0.5 (2) 0.7 (3) 0.3 (4) 0.6 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q6. A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90∘ with respect to each other. The mass of unknown particle is: (1) m (2) m √3 2 (3) 2 m (4) m

Q6. It is found that if a neutron suffers an elastic collinear collision with a deuterium at rest, the fractional loss of its energy is Pd , while for its similar collision with a carbon nucleus at rest, the fractional loss of energy is Pc . The values of Pd and Pc are respectively (1) 0, 1 (2) 0. 89, 0. 28 (3) 0. 28, 0. 89 (4) 0, 0

Q6. The relative uncertainty in the period of a satellite orbiting around the earth is 10−2 . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is: (1) 2 × 10−2 (2) 6 × 10−2 (3) 3 × 10−2 (4) 10−2

Q6. A force of 40 N acts on a point B at the end of an L-shaped object as shown in the figure. The angle θ that will produce the maximum moment of the force about point A is given by: (1) tan θ = 4 (2) tan θ = 14 (3) tan θ = 12 (4) tan θ = 2

Q6. A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by: (1) tan θ = 41 (2) tan θ = 2 (3) tan θ = 12 (4) tan θ = 4

Q7. A thin rod MN , free to rotate in the vertical plane about the fixed end N , is held horizontal. When the end M is released the speed of this end, when the rod makes an angle α with the horizontal, will be proportional to: (see figure) (1) √cos α (2) cos α (3) sin α (4) √sin α

Q7. Suppose that the angular velocity of rotation of the Earth is increased. Then, as a consequence, JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper (1) weight of the object, everywhere on the earth, will (2) weight of the object, everywhere on the earth, will decrease. increase. (3) except at poles, weight of the object on the earth, (4) there will be no change in weight anywhere on will decrease. the earth.

Q7. The mass of a hydrogen molecule is 3.32 × 10−27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of the area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m s−1, then the pressure on the wall is nearly: (1) 4.70 × 102 N m−2 (2) 2.35 × 103 N m−2 (3) 4.70 × 103 N m−2 (4) 2.35 × 102 N m−2

Q7. A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R . And the other mass, in a circular 2 orbit of radius 3R 2 . The difference between the final and the initial total energies is (1) + Gm6R (2) −Gm2R (3) −Gm6R (4) Gm2R

Q8. A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane from opposite sides of the bar with speeds 2v and v respectively. The masses stick to the bar after collision at a distance L and L respectively from the centre of the bar. If the bar 3 6 starts rotating about its center of mass as a result of collision, the angular speed of the bar will be: (1) v (2) 6v 6 L 5 L (3) 3v (4) v 5 L 5 L

Q8. Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: (1) 181 MR2 (2) 19 MR2 2 2 (3) 55 MR2 (4) 73 MR2 2 2

Q8. Take the mean distance of the moon and the sun from the earth to be 0.4 × 106 km and 150 × 106 km, respectively. Their masses are 8 × 1022 kg and 2 × 1030 kg, respectively. The radius of the earth is 6400 km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest point on the earth, and ΔF2 be the difference in the forces exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1 is, ΔF2 (1) 6 (2) 10−2 (3) 2 (4) 0. 6 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q8. A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P2 be the pressure inside the inner bubble and P0 , the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 −P0 between its inside and outside would be: (1) 2 .4 cm (2) 12 cm (3) 4 .8 cm (4) 6 cm