Practice Questions

Q1. A block is placed on a rough horizontal plane. A time dependent horizontal force F = kt acts on the block, where k is a positive constant. The acceleration - time graph of the block is : (1) (2) (3) (4)

Q1. From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is: (1) e2 (2) 4πε0e2 4πε0mc2 me2 (3) me2 (4) 4πε0mc2 4πε0b2 e2

Q2. A 70 kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force F to raise himself. The center of gravity rises by 0.5 m before he leaps. After the leap the c.g. rises by another 1 m . The maximum power delivered by the muscles is : (Take g = 10 ms−2 ) (1) 6.26 × 103 Watts at the start (2) 6.26 × 103 Watts at take off (3) 6.26 × 104 Watts at the start (4) 6.26 × 104 Watts at take off

Q2. A ball projected from ground at an angle of 45∘ just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is : (1) 4.4 m (2) 2.4 m (3) 3.6 m (4) 1.6 m

Q2. Two springs of force constants 300 N/m (Spring A) and 400 N/m (Spring B) are joined together in series. The combination is compressed by 8.75 cm. The ratio of energy stored in A and B is EA . Then EA is equal to: EB EB (1) 4 (2) 16 3 9 (3) 3 (4) 9 4 16

Q2. The maximum range of a bullet fired from a toy pistol mounted on a car at rest is R0 = 40 m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity v = 20 m/s on a horizontal surface? (g = 10 m/s2) (1) 30∘ (2) 60∘ (3) 75∘ (4) 45∘

Q2. A projectile is given an initial velocity of (ˆi 2ˆj) upward. If g = 10 m s−2 , the equation of its trajectory is : (1) 4y = 2x −5x2 (2) 4y = 2x −25x2 (3) y = x −5x2 (4) y = 2x −5x2

Q3. A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be most likely proportional to (1) v4 (2) v2 (3) v (4) v3

Q3. A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart towards the wall, then the final distance of the boy from the wall will be (1) 15 m (2) 12.5 m (3) 15.5 m (4) 17 m

Q3. A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium is : (1) Mg k (1 −LAσ2M ) (2) Mgk (1 + LAσM ) (3) Mg (4) Mg k k (1 −LAσM )

Q3. A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be : (1) 6.25rad/sec (2) 0.625rad/sec (3) 3.35rad/sec (4) 0.335rad/sec

Q3. Two blocks of mass M1 = 20 kg and M2 = 12 kg are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is: (1) 144 N (2) 96 N (3) 240 N (4) 192 N

Q4. A ring of mass M and radius R is rotating about its axis with angular velocity ω. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be : (1) m(M+2m) M ω2R2 (2) (M+m)Mm ω2R2 (3) Mm ω2R2 (4) (M+m)M ω2R2 (M+2m) (M+2m)

Q4. This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M . If the maximum energy loss possible is given as f( 21 mν 2) then f = ( M+mm ). Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision. (1) Statement- I is true, Statement- II is false. (2) Statement- I is false, Statement- II is true. (3) Statement- I is true, Statement- II is true, (4) Statement- I is true, Statement- II is true, Statement- II is a correct explanation of Statement- II is not a correct explanation of Statement- I. Statement- I.

Q4. A uniform sphere of weight W and radius 5 cm is being held by a string as shown in the figure. The tension in the string will be : (1) 12 W5 (2) 5 W12 (3) 13 W5 (4) 13 W12

Q4. A projectile of mass M is fired so that the horizontal range is 4 km . At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is : (1) 16 km (2) 1 km (3) 10 km (4) 2 km

Q4. A body starts from rest on a long inclined plane of slope 45∘ . The coefficient of friction between the body and the plane varies as μ = 0.3x, where x is distance travelled down the plane. The body will have maximum speed (for g = 10 m/s2 ) when x = (1) 9.8 m (2) 27 m (3) 12 m (4) 3.33 m

Q5. A particle of mass 2 kg is moving such that at time t, its position, in meter, is given by →r(t) = 5^i −2t2^j. The angular momentum of the particle at t = 2s about the origin in kgm−2 s−1 is : (1) −80^k (2) (10^i −16^j) (3) −40^k (4) 40^k

Q5. Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If M = 2 m, then the stress JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper produced in the wire is: (1) 2mg (2) 4mg 3 A 3 A (3) mg (4) 3mg A 4 A

Q5. A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of 30∘ with the horizontal. The ball strikes the ground at B. What is the value of JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper the distance AB ? (Moment of inertia of a spherical shell of mass m and radius R about its diameter = 23 mR2 ) (1) 1.87 m (2) 2.08 m (3) 1.57 m (4) 1.77 m

Q5. The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly) : JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper (1) 5 GM (2) 8 GM 6 x2 9 x2 (3) 7 GM (4) 6 GM 8 x2 7 x2

Q5. A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip? (1) rω0 (2) rω0 2 (3) rω0 (4) rω0 4 3

Q6. A body of mass ' m ' is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm . If the angular velocity is doubled, the elongation in the spring is 5 cm . The original length of the spring is : (1) 15 cm (2) 12 cm (3) 16 cm (4) 10 cm

Q6. In an experiment, a small steel ball falls through a liquid at a constant speed of 10 cm/s. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? (1) 5 cm/s (2) Zero (3) 10 cm/s (4) 20 cm/s

Q6. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R? (1) GmM (2) GmM 2R 3R (3) 5GmM (4) 2GmM 6R 3R