Practice Questions

Q1. Dimensional formula for thermal conductivity is (here K denotes the temperature): (1) MLT –2K (2) MLT –2K–2 (3) MLT –3K (4) MLT –3K–1

Q1. The quantities x = 1 , y = EB and z = CRl are defined where C-capacitance, R-Resistance, ℓ−length, E- √μ0∈0 Electric field, B-magnetic field and ∈0, μ0, −free space permittivity and permeability respectively. Then: (1) x, y and z have the same dimension. (2) Only x and z have the same dimension (3) Only x and y have the same dimension (4) Only y and z have the same dimension.

Q1. A physical quantity z depends on four observables a, b, c and d , as z = a2b2/3 . The percentage of error in the √cd3 measurement of a, b, c and d are 2%, 1. 5%, 4% and 2. 5% respectively. The percentage of error in z is : (1) 12. 25% (2) 16. 5% (3) 13. 5% (4) 14. 5%

Q1. A 60HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 m s−2) (1) 1.7 m s−1 (2) 1.9 m s−1 (3) 1.5 m s−1 (4) 2.0 m s−1

Q1. If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is : (1) [P2 AT−2] (2) [PA−1 T −1] (3) [PA1/2 T−1] (4) [P 1/2 AT−1]

Q1. If speed V , area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be : (1) FA2 V−1 (2) FA2 V−3 (3) FA2 V−2 (4) FA−1 V0

Q1. Moment of inertia of a cylinder of mass m, length L and radius R about an axis passing through its centre and L2 If such a cylinder is to be made for a given mass perpendicular to the axis of the cylinder is I = + M( R24 12 ). of a material, the ratio L for it to have minimum possible I is: R (1) 2 (2) 3 3 2 (3) √32 (4) √23

Q1. where c is speed of light, G univasal gravitational constant and h is the A quantity f is given by f = √hc5G Planck’s constant. Dimension of f is that of: (1) area (2) energy (3) momentum (4) volume →

Q1. A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stopwatch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is: (1) 5.40% (2) 3.40% (3) 4.40% (4) 2.40%

Q2. Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of the system is at a point: (1) 0.6 cm right and 2.0 cm above 1 kg mass. (2) 1.5 cm right and 1.2 cm above 1 kg mass. (3) 2.0 cm right and 0.9 cm above 1 kg mass. (4) 0.9 cm right and 2.0 cm above 1 kg mass.

Q2. The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4. 333 seconds. The total distance covered by the body in 6 s is : (1) 37 3 m (2) 12m (3) 11m (4) 494 m

Q2. A balloon is moving up in air vertically above a point A on the ground. When it is a height h1, a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45° with respect to the vertical. When the balloon climbs up a further height h2 , it is seen at an angle 60° with respect to the vertical if the girl moves further by a distance 2. 464 d (point C). Then the height h2 is (given tan 30°= 0. 5774): (1) 1. 464 d (2) 0. 732 d (3) 0 .464 d (4) d

Q2. An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg . The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s . The frictional force opposing the motion is 6000 N . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10m/s2) must be at least: (1) 56300W (2) 62360W (3) 48000W (4) 66000W

Q2. A particle is moving unidirectional on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) – time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale): (1) (2) (3) (4)

Q2. An insect is at the bottom of a hemispherical ditch of radius 1m . It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0. 75, then his : (g = 10 m s−2) (1) 0. 20 m (2) 0. 45 m (3) 0. 60 m (4) 0. 80 m

Q2. A spring mass system (mass m, spring constant k and natural length l ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system rotates about it's axis with an angular velocity ω, (k >> mω2) the relative change in the length of the spring is best given by the option: (1) mω2 (2) 2mω2 k √23 ( k ) (3) mω2 (4) mω2 k 3k

Q2. Consider a force F = −xˆi + yˆj . The work done by this force in moving a particle from point A(1,0) to B(0,1) along the line segment is : (all quantities are in SI units) (1) 2 (2) 21 (3) 1 (4) 32

Q2. When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops coming at an angle 60∘ from the horizontal. On further increasing the speed of the car to (1 + β)v, this angle changes to 45∘ . The value of β is close to : (1) 0. 50 (2) 0. 41 (3) 0. 37 (4) 0. 73 B of mass m2

Q2. A tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height h/2. The velocity versus height of the ball during its motion may be represented graphically by: (graphs are drawn schematically and on not to scale) (1) (2) (3) (4)

Q2. A particle of charge q and mass m is subjected to an electric field E = E0(1–ax2) in the x−direction, where a and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is : (1) a (2) √2a (3) √3a (4) √1a

Q2. Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0. 1 kg −m2 and 10 rad s−1 respectively while those for the second one are 0. 2 kg −m2 and 5 rad s−1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is : (1) 10 3 J (2) 203 J (3) 3 5 J (4) 23 J

Q3. A particle moves such that its position vector →r(t) = cos ωtˆi + sin ωtˆj where ω is a constant and t is time. Then which of the following statements is true for the velocity →v(t) and acceleration →a(t) of the particle: (1) →vis perpendicular to →rand →a is directed away (2) →vand →a both are perpendicular to →r from the origin (3) →vand →a both are parallel to →r (4) →vis perpendicular to →rand →a is directed towards the origin

Q3. The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass 4 kg. (The coordinates of the same are shown in the figure) are: (1) (1.25 m, 1.50 m) (2) (0.75 m, 1.75 m) (3) (0.75 m, 0.75 m) (4) (1 m, 1.75 m)

Q3. If the potential energy between two molecules is given by U = A + B , then at equilibrium, separation r6 r12 between molecules, and the potential energy are: (1) ( 2AB ) 1/6, −A22B (2) ( AB ) 1/6, 0 1 A2 , B ) 6 (3) ( 2BA ) 1/6, 4BA2 (4) ( 2A 2B

Q3. As shown in the figure, a bob of mass m is tied to a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be: (1) 1 gh (2) 3 r √4 3 r√ 2 gh (3) 1 gh (4) 3 r √2 3 r√ 4 gh