Practice Questions

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. Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is: (1) ML2 T−2 (2) ML0 T−3 (3) M2L0T−1 (4) MLT−2

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. 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. 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. For the four sets of three measured physical quantities as given below. Which of the following options is correct? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 = 236.183 (iv) A4 = 25, B4 = 236.191, C4 = 19.5 (1) A4 + B4 + C4 < A1 + B1 + C1 < A3 + B3 + C3 < A2 + B2 + C2 (2) A1 + B1 + C1 = A2 + B2 + C2 = A3 + B3 + C3 = A4 + B4 + C4 (3) A1 + B1 + C1 < A2 + B2 + C2 = A3 + B3 + C3 < A4 + B4 + C4 (4) A1 + B1 + C1 < A3 + B3 + C3 < A2 + B2 + C2 < A4 + B4 + C4

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. 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%

Q1. Given, B is magnetic field induction, and μ0 is the magnetic permeability of vacuum. The dimension of B2 is: 2μ0 (1) MLT−2 (2) ML2T−1 (3) ML2T−2 (4) ML−1T−2

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. 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

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. 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. Train A and train B are running on parallel tracks in the opposite directions with speed of 36 km hour−1 and 72 km hour−1 , respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1. 8 km hour−1 . Speed (in m s−1) of this person as observed from train B will be close to: (take the distance between the tracks as negligible) (1) 29. 5 m s−1 (2) 28. 5 m s−1 (3) 31. 5 m s−1 (4) 30. 5 m s−1

Q2. A block of mass m = 1 kg slides with velocity v = 6 m s−1 on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. if the rod has mass M = 2 kg, and length ℓ= 1 m, the value of θ is approximately (take g = 10 m s−2) (1) 63° (2) 55° (3) 69° (4) 49°

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. 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. A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is: (1) mlω2 (2) mlω2 k−ωm k−mω2 (3) mlω2 (4) mlω2 k+mω2 k+mω

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. 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 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. A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale) (1) (2) (3) (4)

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. 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. 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