Practice Questions

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

Q1. The dimensions of angular momentum, latent heat and capacitance are, respectively. (1) ML2 T1 A2, L2 T−2, M−1 L−2 T2 (2) ML2 T−2, L2 T2, M−1 L−2 T4 A2 (3) ML2 T−1, L2 T−2, ML2TA2 (4) ML2 T−1, L2 T−2, M−1 L−2 T4 A2

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. If the time period t of the oscillation of a drop of liquid of density d, radius r, vibrating under surface tension s . The is given by the formula t = √r2bscda/2 . It is observed that the time period is directly proportional to √ds value of b should therefore be : (1) 3 (2) √3 4 (3) 3 (4) 2 2 3

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

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 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

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. 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. 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 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

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 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 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)

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

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 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

Q6. If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is : (1) 3c (2) 2a2c 2ab2 b (3) 3a (4) 2ac 2b2c b2

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. The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon = 7.36 × 1022 kg, radius of the moon's orbit = 3.8 × 108 m ). (1) 6.73 × 10−5 m/s2 (2) 6.73 × 10−3 m/s2 (3) 6.73 × 10−2 m/s2 (4) 6.73 × 10−4 m/s2