Practice Questions

Q3. Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0. 15. The minimum weight m that should be put on top of m2 to stop the motion is: (1) 10 .3 kg (2) 18 .3 kg (3) 27 .3 kg (4) 43 .3 kg

Q3. A body of mass m starts moving from rest along x−axis so that its velocity varies as v = a√s where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t second after the start of the motion is (1) 8 ma4t2 (2) 14 ma4t2 (3) 4 ma4t2 (4) 18 ma4t2

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

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. 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. 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 √

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 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 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 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

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

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. 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

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. 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

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. 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. 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.

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

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

Q9. When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5r . Taking the 4 atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature): (1) 10.5 m (2) 8.7 m (3) 11.2 m (4) 9.5 m

Q9. One mole of an ideal monatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by: (1) 25 P0V0 (2) 5 P0V0 4 R 8 R (3) 25 P0V0 (4) 25 P0V0 8 R 16 R

Q9. A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are ρ1 and ρ2 (ρ1 > ρ2 ), fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is: θ = (1) θ = tan−1 π2 ( ρ1−ρ2ρ1+ρ2 ) (2) tan−1[( ρ1+ρ2ρ1−ρ2 )] θ = (3) θ = tan−1 π2 ( ρ2ρ1 ) (4) tan−1π( ρ2ρ1 )

Q9. From a uniform circular disc of radius R and mass 9 M, a small disc of radius R is removed as shown in the 3 figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is: (1) 37 MR2 (2) 4MR2 9 (3) 40 MR2 (4) 10MR2 9

Q10.Two moles of helium are mixed with n moles of hydrogen. If Cp = 32 for the mixture then the value of n is, Cv (1) 1 (2) 3 (3) 2 (4) 3 2