Practice Questions

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

Q3. A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of dM dt = αv where M is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is (1) −αv22M (2) −αv2M (3) −αv2 (4) −2αv2M

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

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. A projectile moving vertically upwards with a velocity of 200 ms−1 breaks into two equal parts at a height of 490 m. One part starts moving vertically upwards with a velocity of 400 ms−1 . How much time it will take, after the break up with the other part to hit the ground? (1) 2√10 s (2) 5 s (3) 10 s (4) √10 s

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 ),

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. 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

Q5. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2 , respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is (1) m1r1 : m2r2 (2) m1 : m2 (3) r1 : r2 (4) 1 : 1

Q5. Two bodies A and B of mass m and 2m respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body C of mass m is placed on the floor. The body C moves with a velocity v0 along the line joining A and B and collides elastically with A . At a certain time after the collision it is found JEE Main 2012 (12 May Online) JEE Main Previous Year Paper that the instantaneous velocities of A and B are same and the compression of the spring is x0 . The spring constant k will be v0 v20 (2) m (1) m 2x0 x2 0 (3) 2m v0 (4) 2 v0 2 x0 3 m( x0 )

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

Q5. A particle gets displaced by Δ¯r = (2^i + 3^j + 4^k)m under the action of a force →F = (7^i + 4^j + 3^k). The change in its kinetic energy is (1) 38 J (2) 70 J (3) 52.5 J (4) 126 J

Q5. Two point masses of mass m1 = fM and m2 = (1 −f)M(f < 1) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω1 for m1 and ω2 for m2 . In that case (1) (1 −f)ω1 = fω (2) ω1 = ω2 and independent of f (3) fω1 = (1 −f)ω2 (4) ω1 = ω2 and depend on f

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. 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 circular hole of diameter R is cut from a disc of mass M and radius R; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is (1) ( 1532 )MR2 (2) ( 18 )MR2 (3) ( 83 )MR2 (4) ( 1332 )MR2

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 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 steel wire can sustain 100 kg weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of (1) 50 kg (2) 400 kg (3) 100 kg (4) 200 kg

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 thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5 × 10−2 N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is (1) 0.0125 Nm−1 (2) 0.1 Nm−1 (3) 0.05 Nm−1 (4) 0.025 Nm−1

Q7. A thick-walled hollow sphere has outside radius R0 . It rolls down an incline without slipping and its speed at the bottom is v0 . Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be 5v0/4 . The radius of gyration of the hollow sphere about an axis through its centre is (1) 3R0/2 (2) 3R0/4 (3) 9R0/16 (4) 3R0

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. Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth = RE )? (1) (2) (3) (4)