Practice Questions

Q2. Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure: −−→ → The relative velocity VA −VB at t = 2ωπ is given by: (1) ω (R1 + R2)^i (2) −ω (R1 + R2)^i (3) ω (R2 −R1)^i (4) ω (R1 −R2)^i

Q3. A block of mass 10 𝑘𝑔 is kept on a rough inclined plane as shown in the figure. A force of 3 𝑁 is applied on the block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum value of force 𝑃, such that the block does not move downward? (take 𝑔= 10 𝑚𝑠-2 ) (1) 23 𝑁 (2) 25 𝑁 (3) 18 𝑁 (4) 32 𝑁

Q3. A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30o with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is μ = 0.2. The difference between the accelerations of the block, in case (B) and case (A) will be: (g = 10 m s−2) (1) 3.2 m s−2 (2) 0 m s−2 (3) 0.8 m s−2 (4) 0.4 m s−2

Q3. A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is: [Take g = 10 m/s2 ] (1) √3 (2) 2 4 3 (3) 1 (4) √3 2 2

Q3. The position vector of a particle changes with time according to the relation →r(t) = 15t2ˆi + (4 −20t2)ˆj. What is the magnitude of the acceleration at t = 1? (1) 40 (2) 25 (3) 100 (4) 50

Q3. If Surface tension ( S ) , Moment of Inertia ( I ) and Planck's constant ( h ) , were to be taken as the fundamental units, the dimensional formula for linear momentum would be: (1) S1 / 2I1 / 2h0 (2) S1 / 2I3 / 2h-1 (3) S3 / 2I1 / 2h0 (4) S1 / 2I1 / 2h-1

Q3. Two forces P and Q, of magnitude 2F and 3F , respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is: (1) 120° (2) 60° (3) 30° (4) 90°

Q3. A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is: (1) R / 2g (2) R / g (3) 2R / g (4) R / 4g

Q3. Two particles of masses M and 2M are moving with speeds of 10 m s−1 and 5 m s−1 , as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds v1 and v2 , respectively. The values of v1 and v2 are, nearly (1) 6.5 m s−1 and 3.2 m s−1 (2) 3.2 m s−1 and 12.6 m s−1 (3) 13.02 m s−1 and 19. 7 m s−1 (4) 3.2 m s−1 and 6.3 m s−1

Q3. A plane is inclined at an angle α = 30° with respect to the horizontal. A particle is projected with a speed u = 2 m s-1 , from the base of the plane, making an angle θ = 15° with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to: (Take g = 10 m s-2 ) (1) 20 cm (2) 18 cm (3) 14 cm (4) 26 cm

Q4. Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficients of friction between A and B is 0.2 and between B and the surface of the table is also 0.2 . The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : [Take g = 10 m / s2 ] (1) 16 N (2) 12 N (3) 40 N (4) 8 N 7M

Q4. If 1022 gas molecules each of mass 10-26 kg collides with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104m / s, the pressure exerted by the gas molecules will be of the order of: (1) 2 Pa (2) 4 Pa (3) 6 Pa (4) 8 Pa

Q4. A block of mass 𝑚, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant 𝑘. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force 𝐹, the maximum speed of the block is: 𝐹 2𝐹 (1) (2) √𝑚𝑘 √𝑚𝑘 (3) 𝜋𝐹 (4) 𝐹 √𝑚𝑘 𝜋√𝑚𝑘

Q4. A spring whose unstrentches length is l has a force constant k. The spring is cut into two pieces of unstretches lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constants, k1 and k2 will be: (1) 1 (2) n2 n2 (3) n (4) n1

Q4. A thin disc of mass M and radius R has mass per unit area σ(r) = kr2 where r is the distance from its centre. Its moment inertia about an axis going through its centre of mass and perpendicular to its plane is: (1) MR2 (2) MR2 3 2 (3) MR2 (4) 2MR2 6 3

Q4. A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by: (1) v2 (2) v2 g 2g (3) 2v2 (4) 2v2 5g 7g

Q4. A block of mass m is kept on a platform which starts from rest with a constant acceleration g/2 upwards, as shown in the figure. Work done by normal reaction on block in time t is (1) −mg2t28 (2) m g2t28 (3) 0 (4) 3 m g2t2 8

Q4. A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 m s−2) (1) 100 N (2) 200 N (3) 140 N (4) 70 N

Q4. The position vector of the center of mass→rcm of an asymmetric uniform bar of negligible area of cross-section as shown in figure is: 13 (1)→rcm = 8 L^x + 85 Lˆy (2)→rcm = 8 5 L^x + 138 Lˆy 11 (3) →rcm = 8 3 L^x + 118 Lˆy (4)→rcm = 8 L^x + 83 Lˆy

Q4. A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is l1, and that below the piston is l2, such that l1 > l2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass m will be given by: ( R is universal gas constant and g is the acceleration due to gravity) (1) RT l1−3l2 (2) nRT l1−l2 ng [ l1l2 ] g [ l1l2 ] (3) RT 2l1+l2 (4) RT 2l1+l2 g [ l1l2 ] gl [ l1l2 ]

Q4. A uniform cable of mass M and length L is placed on a horizontal surface such that its ( n1 ) th below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be: (1) MgL (2) MgL 2n2 n2 (3) nMgL (4) 2MgL n2

Q4. A man (mass = 50 kg ) and his son (mass = 20 kg ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 m s-1 with respect to the man. The speed of the man with respect to the surface is: (1) 0.20 m s-1 (2) 0.14 m s-1 (3) 0.47 m s-1 (4) 0.28 m s-1

Q5. Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm ), about its axis be I . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is: (1) 16 cm (2) 14 cm (3) 12 cm (4) 18 cm

Q5. Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be: √3 √3 m, m, (1) ( 127 4 m) (2) ( 127 8 m) (3) ( √34 m, 125 m) (4) ( √38 m, 127 m)

Q5. Two coaxial discs, having moments of inertia I1 and I12 , are rotating with respective angular velocities ω1 and ω1 , about their common axis. They are brought in contact with each other and thereafter they rotate with a 2 common angular velocity. If Ef and Ei are the final and initial total energies, then (Ef −Ei) is: (1) I1ω2 1 (2) 3 8 I1ω21 6 1 (3) − I1ω212 1 (4) − I1ω224 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper