Practice Questions

Q1. An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be : (1) 4.4% (2) 2.27% (3) 1.7% (4) 2.7%

Q1. From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is: (1) ch (2) e2 2πε2o 2πεoGm2e (3) μoεo G (4) 2π√μoεo h c2 he2 ce2 G

Q1. In terms of resistance R and time T , the dimensions of ratio με of the permeability μ and permittivity ε is: (1) [RT−2] (2) [R2 T−1] (3) [R2] (4) [R2 T2]

Q2. The position of a projectile launched from the origin at t = 0 is given by→r= (40 ˆi + 50 ˆj)m at t = 2s. If the projectile was launched at an angle θ from the horizontal, then θ is (take g = 10 ms-2). (1) tan−1 23 (2) tan−1 32 (3) tan−1 74 (4) tan−1 45

Q2. A person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator? (1) 37 s (2) 27 s (3) 24 s (4) 45 s

Q2. A heavy box is to be dragged along a rough horizontal floor. To do so, the person A pushes it at an angle 30° from the horizontal and requires a minimum force FA , while the person B pulls the box at an angle 60° from the horizontal and needs minimum force FB . If the coefficient of friction between the box and the floor is √35 , the ratio FA is FB (1) √32 (2) √32 (3) √3 (4) 5 √3

Q2. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path.The relation between H, u and n is : (1) 2 g H = n2u2 (2) g H = (n - 2)2u2 (3) 2g H = nu2(n - 2) (4) g H = (n - 2)u2

Q2. The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target ? (1) 1.0 m (2) 4.2 m (3) 6.1 m (4) 9.8 m

Q3. A block of mass m is placed on a surface with a vertical cross section given by y = x36 . If the coefficient of friction is 0. 5, the maximum height above the ground at which the block can be placed without slipping is (1) 1 6 m (2) 32 m (3) 3 1 m (4) 21 m

Q3. A body of mass 5 kg under the action of constant force →F = Fx^i + Fy^j has velocity at t = 0 s as →v = (6^i −2^jm/s) and at t = 10 s as →v = +6^jm/s. The force →F is: (1) (−3^i + 4^j)N (2) (−35^i + 45 ^j)N (3) (3^i −4^j)N (4) ( 5^i3 −45^j)N

Q3. A particle is released on a vertical smooth semicircular track from point X so that, OX makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point Y where OY makes an angle ϕ with the horizontal. Then (1) sinϕ = 23 cosθ (2) sinϕ = 34 cosθ (3) sinϕ = 12 cosθ (4) sinϕ = cosθ

Q3. Water is flowing at a speed of 1.5 m s-1 through a horizontal tube of cross-sectional area 10-2 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = 103 kg m-3) (1) 33.7 N (2) 45 N (3) 15 N (4) 22.5 N

Q4. A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be : (1) 0 N (2) 25 N (3) 48 N (4) 27 N

Q4. A small ball of mass m starts at a point A with speed vo and moves along a frictionless track AB as shown. The track BC has coefficient of friction μ. The ball comes to stop at C after travelling a distance L which is: v20 (1) 2 o (2) μ h + 2μgv2 μ h + 2μg (3) 2μ h + μgv2o (4) 2μh + 2μgv2o

Q4. A spring of unstretched length 1 has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is: (1) 1 mv2 (2) mv2 2 (3) 1 3 mv2 (4) 16 mv2

Q4. Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is Ffriction at point P ? It is assumed that the cylinder does not slip. (1) Ma (2) Ma2 (3) Ma (4) Mg 3

Q4. When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx2 where a and b are constants. The work done in stretching the unstretched rubber-band by L is : (1) aL2 + bL3 (2) 12 (aL2 + bL3) bL3 bL3 (3) aL2 (4) + 2 + 3 2 1 ( aL22 3 )

Q5. A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio sinθc sinθs is : (1) 8 (2) 7 √87 (3) (4) 15 14 √1514

Q5. A thin bar of length L has a mass per unit length λ, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λO , then the distance of the centre of mass from the lighter end is: (1) L 2 −λ04ML2 (2) L3 + λ08ML2 (3) L 3 + λ04ML2 (4) 23L −λ06ML2

Q5. Three masses m, 2 m and 3 m are moving in x −y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: (1) 12 u (^i + √3^j) (2) 12u (^i −√3^j) (3) 12 u (−^i + √3^j) (4) 12u (−^i −√3^j)

Q5. A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 m s−1 . The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 m s−2) JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) 1. 73 kg m2 s−1 (2) 3. 46 kg m2 s−1 (3) 3. 0 kg m2 s−1 (4) 6. 0 kg m2 s−1

Q5. A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? (1) 2g (2) g 3 2 (3) 5g (4) g 6

Q6. A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by ' C '. The angular momentum from the origin O can be written as: JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) va (1 + cos 2θ) (2) va (1 + cos θ) (3) va cos 2θ (4) va

Q6. A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension : (1) Angular momentum is conserved (2) Angular momentum changes in magnitude but not in direction (3) Angular momentum changes in direction but not (4) Angular momentum changes both in direction and in magnitude magnitude

Q6. From a sphere of mass M and radius R, a smaller sphere of radius R2 is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is: (1) 41GM2 (2) 41GM2 3600R2 450R2 (3) 59GM2 (4) GM2 450R2 225R2 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper