Practice Questions

Q1. In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be: (1) 1 a (2) 1 2 (ˆk −ˆi) 2 a(ˆi −ˆk) (3) 1 (4) 1 2 a(ˆj −ˆi) 2 a(ˆj −ˆk)

Q1. A particle is moving with speed v = b√x along positive x− axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0 ) (1) b2τ (2) b2τ √2 (3) b2τ (4) b2τ 2 4

Q1. A particle is moving with a velocity →𝑣= 𝐾𝑦^𝑖+ 𝑥^𝑗, where 𝐾 is a constant. The general equation for its path is: (1) 𝑦2 = 𝑥+ constant (2) 𝑥𝑦= constant (3) 𝑦= 𝑥2 + constant (4) 𝑦2 = 𝑥2 + constant

Q1. Which of the following combinations has the dimension of electrical resistance ( ϵ0 is the permittivity of vacuum and μ0 is the permeability of vacuum)? ϵ0 ϵ0 (1) (2) μ0 √ μ0 μ0 μ0 (3) (4) ϵ0 √ ϵ0

Q1. The position co-ordinates of a particle moving in a 3D coordinate system is given by x = a cos ωt y = a sin ωt and z = aωt The speed of the particle is: (1) √2 aω (2) aω (3) 2aω (4) √3 aω

Q1. In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is: (1) 0.31 (2) 0.10 (3) 0.07 (4) 0.01

Q1. The force of interaction between two atoms is given by F = αβ exp (−x2αkT ); where Boltzmann constant and T is temperature and α and β are two constants. The dimensions of β is: (1) M0 L2 T−4 (2) M2LT−4 (3) MLT−2 (4) M2 L2 T−2

Q1. In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units? (1) M-1 L-2 T4 A2 (2) M-2 L0 T-4 A-2 (3) M-2 L-2 T6 A3 (4) M-3 L-2 T8 A4

Q1. A particle moves from the point (2.0^i + 4.0^j)m, at t = 0 , with an initial velocity (5.0^i + 4.0^j)ms−1. It is acted upon by a constant force which produces a constant acceleration (4.0^i + 4.0^j)ms−2. What is the distance of the particle from the origin at time 2 s? (1) 15 m (2) 20√2 m (3) 5 m (4) 10√2 m

Q1. The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm , respectively. What will be the value of its volume in appropriate significant figures? (1) 4264 ± 81cm3 (2) 4264.4 ± 81.0 cm3 (3) 4260 ± 80 cm3 (4) 4300 ± 80 cm3 → → → →

Q1. Ship A is sailing towards north-east with velocity) →𝑣= 30 ^i + 50 ^j km h-1 where ^i points east and ^j, north. The ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards the west at 10 km h-1 . A will be at the minimum distance from B in: (1) 4.2 h (2) 3.2 h (3) 2.6 h (4) 2.2 h

Q1. Let →A1 = 3, →A2 = 5 and →A1 + →A2 = 5 . The value of 2→A1 + 3→A2 ∙3→A1 - 2→A2 is: (1) -112.5 (2) -118.5 (3) -106.5 (4) -99.5

Q1. A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level, but he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is: (1) 2v (2) v √3 (3) v (4) √3 v 2 2

Q2. A passenger train of length 60 m travels at a speed of 80 km / hr. Another freight train of length 120 m travels at a speed of 30 km / hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is: (1) 5 (2) 3 2 2 (3) 11 (4) 25 5 11

Q2. Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to: (1) √Ghc3 (2) √hc5G (3) √Ghc5 (4) √c3Gh

Q2. In SI units, the dimensions of ϵ0 is: √ μ0 (1) AT2M-1L-1 (2) A2T3M-1L-2 (3) A-1TML3 (4) AT-3ML3 / 2

Q2. In a simple pendulum experiment for determination of acceleration due to gravity ( g ) , time taken for 20 oscillations is measures by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of the pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to (1) 0.2% (2) 6.8% (3) 3.5% (4) 0.7%

Q2. The density of a material in SI units is 128 kg m−3. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is: (1) 410 (2) 16 (3) 40 (4) 640

Q2. If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be : (1) V−2 A2 F−2 (2) V−2 A2 F2 (3) V−4 A−2 F (4) V−4 A2 F

Q2. A particle is moving along a circular path with a constant speed of 10 ms−1 . What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60∘ around the centre of the circle? (1) 10√3 m/s (2) zero (3) 10√2 m/s (4) 10 m/s

Q2. The trajectory of a projectile near the surface of the earth is given as 𝑦= 2𝑥- 9𝑥2 . If it were launched at an angle θ0 with speed 𝑣0 then g = 10 m s-2: 1 5 2 3 (1) θ0 = cos-1⁡ √5 and 𝑣0 = 3 ms-1 (2) θ0 = cos-1⁡√5 and 𝑣0 = 5 ms-1 1 5 2 3 (3) θ0 = sin-1⁡ √5 and 𝑣0 = 3 ms-1 (4) θ0 = sin-1⁡√5 and 𝑣0 = 5 ms-1

Q2. Two vectors A and B have equal magnitudes. The magnitude of A + is ' n ' times the magnitude of ( B) → → → → A − . The angle between A and B is: ( B) n+1 ] (1) cos−1[ n2−1n2+1 ] (2) sin−1[ n−1 (3) cos−1[ n−1n+1 ] (4) sin−1[ n2−1n2+1 ]

Q2. Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct? (1) R2 = h1h2 (2) R2 = 4 h1h2 (3) R2 = 2 h1h2 (4) R2 = 16 h1h2

Q2. Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure: −−→ → The relative velocity VA −VB at t = 2ωπ is given by: (1) ω (R1 + R2)^i (2) −ω (R1 + R2)^i (3) ω (R2 −R1)^i (4) ω (R1 −R2)^i

Q2. A bullet of mass 20 g has an initial speed of 1 m s-1, just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10-2 N, the speed of the bullet after emerging from the other side of the wall is close to: (1) 0.7 m s-1 (2) 0.3 m s-1 (3) 0.1 m s-1 (4) 0.4 m s-1