Practice Questions

Q2. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be (1) 20√2 m (2) 10 m (3) 10√2 m (4) 20 m

Q2. The distance travelled by a body moving along a line in time t is proportional to t3 . The acceleration-time (a, t) graph for the motion of the body will be (1) (2) (3) (4)

Q3. A particle of mass m is at rest at the origin at time t = 0 . It is subjected to a force F(t) = F0e−bt in the x direction. Its speed v(t) is depicted by which of the following curves? (1) (2) (3) (4)

Q3. An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3 . If the line joining the centre of the hemispherical surface to the insect makes an angle α with the vertical, the maximum possible value of α so that the insect does not slip is given by (1) cot α = 3 (2) sec α = 3 (3) cosec α = 3 (4) cos α = 3

Q3. Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of 3 ms−1 will be (1) 12 N (2) 6 N (3) zero (4) 18 N

Q3. A car of mass 1000 kg is moving at a speed of 30 m/s . Brakes are applied to bring the car to rest. If the net retarding force is 5000 N , the car comes to stop after travelling d m in t s . Then (1) d = 150, t = 5 (2) d = 120, t = 8 (3) d = 180, t = 6 (4) d = 90, t = 6

Q4. An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is (1) mv3 (2) mv2 (3) 1 mv2 (4) 1 mv3 2 2

Q4. This question has statement 1 and statement 2 . Of the four choices given after the statements, choose the one that best describes the two statements. If two springs S1 and S2 of force constants k1 and k2 , respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2 . Statement 1 : If stretched by the same amount, work done on S1 , will be more than that on S2 Statement 2 : k1 < k2 (1) Statement 1 is false, Statement 2 is true (2) Statement 1 is true, Statement 2 is false (3) Statement 1 is true, Statement 2 is the correct (4) Statement 1 is true, Statement 2 is true, Statement explanation for statement 1 2 is not the correct explanation for statement 1.

Q4. This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force. Statement 2: The cart does not move because the force described in statement 1 cancel each other. JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) Statement 1 is true, Statement 2 is true, Statement (2) Statement 1 is false, Statement 2 is true. 2 is the correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

Q4. A block of weight W rests on a horizontal floor with coefficient of static friction μ. It is desired to make the block move by applying minimum amount of force. The angle θ from the horizontal at which the force should be applied and magnitude of the force F are respectively. μW (1) θ = tan−1(μ), F = F = √1+μ2 μW (2) θ = tan−1 ( μ1 ), √1+μ2 F = 1+μμW (3) θ = 0, F = μW (4) θ = tan−1 ( 1+μμ ),

Q5. The force →F = F^i on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x = 0. What is the kinetic energy of the particle at x = 8 m? (1) 34 J (2) 34.5 J (3) 4.5 J (4) 29.4 J

Q6. The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of ' g ' and ' R ' (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be ; (1) 6.4 × 1011 Joules (2) 6.4 × 108 Joules (3) 6.4 × 109 Joules (4) 6.4 × 1010 Joules JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q6. A spring is compressed between two blocks of masses m1 and m2 placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of v1 and v2 as shown. The blocks travel distances x1 and x2 respectively before coming to rest. The ratio ( x1x2 ) is (1) m2 (2) m1 m1 m2 (3) √m2m1 (4) √m1m2

Q6. A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T = Arn , where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to (1) −1 (2) −2 (3) −4 (4) −3

Q6. A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to (1) 33% (2) 67% (3) 90% (4) 10%

Q7. A solid sphere is rolling on a surface as shown in figure, with a translational velocity v m s−1 . If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is (1) √2gh (2) √75 gh (3) (4) gh gh √72 √107

Q7. A solid sphere having mass m and radius r rolls down an inclined plane. Then its kinetic energy is (1) 5 rotational and 2 translational (2) 2 rotational and 5 translational 7 7 7 7 (3) 2 rotational and 3 translational (4) 1 rotational and 1 translational 5 5 2 2 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

Q8. A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C . When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be (1) √2Gmr (√2 −1 (2) √Gmr − √2Gmr r (1 √2 ) (3) √2Gm 1 (4)

Q8. This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: When moment of inertia I of a body rotating about an axis with angular speed ω increases, its angular momentum L is unchanged but the kinetic energy K increases if there is no torque applied on it. Statement 2: L = Iω, kinetic energy of rotation = 12 Iω2 JEE Main 2012 (12 May Online) JEE Main Previous Year Paper (1) Statement 1 is true, Statement 2 is true, Statement (2) Statement 1 is false, Statement 2 is true. 2 is not the correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is true, Statement (4) Statement 1 is true, Statement 2 is false. 2 is correct explanation of the Statement 1.

Q9. A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100kN force stretches it along its length. Young's modulus of structural steel is 2 × 1011Nm−2 . The percentage strain is about (1) 0.16% (2) 0.32% (3) 0.08% (4) 0.24%

Q9. A liquid in a beaker has temperature θ(t) at time t and θ0 is temperature of surroundings, then according to Newton's law of cooling the correct graph between loge (θ −θ0) and t is JEE Main 2012 (Offline) JEE Main Previous Year Paper (1) (2) (3) (4)

Q9. A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length ( L2 ) each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at 100∘C and that of steel at 0∘C then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel) (1) 90∘C (2) 50∘C (3) 10∘C (4) 67∘C

Q10.In a cylindrical water tank, there are two small holes A and B on the wall at a depth of h1 , from the surface of water and at a height of h2 from the bottom of water tank. Surface of water is at height of h2 from the bottom of water tank. Surface of water is at heigh H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S . Find the ratio of h1 and h2 (1) Depends on H (2) 1 : 1 (3) 2 : 2 (4) 1 : 2

Q10.The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line (1) OA (2) OC (3) OD (4) OB

Q10.Water is flowing through a horizontal tube having cross-sectional areas of its two ends being A and A′ such that the ratio A/A′ is 5 . If the pressure difference of water between the two ends is 3× 105 N m−2 , the velocity of water with which it enters the tube will be (neglect gravity effects) (1) 5 m s−1 (2) 10 m s−1 (3) 25 m s−1 (4) 50√10 m s−1