Practice Questions

Q1. Let A = + and B = − . The magnitude of a coplanar vector C such that (ˆi ˆj) (2ˆi ˆj) → → → → → → A . C = B. C = A . B is given by: (1) √912 (2) √209 (3) √59 (4) √109

Q1. The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1. 5% and 1%, respectively, the maximum error in determining the density is: (1) 6 % (2) 2.5 % (3) 3.5 % (4) 4.5 %

Q2. An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding) (1) 75 m (2) 160 m (3) 100 m (4) 150 m

Q2. A man in a car at location Q on a straight highway is moving with speed v . He decides to reach a point P in a field at a distance d from highway (point M ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum? (1) d (2) d √3 2 (3) d (4) d √2

Q2. All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up. (1) (2) (3) (4)

Q2. The percentage errors in quantities P , Q , R and S are 0. 5%, 1%, 3% and 1. 5% respectively in the P 3Q2 measurement of a physical quantity A= . The maximum percentage error in the value of A will be: √RS (1) 6.5 % (2) 7.5 % (3) 6.0 % (4) 8.5 %

Q2. The velocity time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively. (1) 112. 5 m and 22. 5 s (2) 337. 5 m and 25 s (3) 225. 5 m and 10 s (4) 112. 5 m and 15 s

Q3. The velocity-time graphs of a car and a scooter are shown in the figure. (i) the difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively (1) 337.5 m and 25 s (2) 225.5 m and 10 s (3) 112.5 m and 22.5 s (4) 112.5 m and 15 s

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

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. 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. 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. 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 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. 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 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

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. 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. 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 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

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 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. 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