Practice Questions

Q1. The de-Broglie wavelength associated with a particle of mass m and energy E is h/√2mE . The dimensional formula for Planck's constant is : (1) [ML2 T−1] (2) [ML−1 T−2] (3) [MLT−2] (4) [M2 L2 T−2]

Q1. Match List-I with List-II. List-I List-II A. Coefficient of viscosity I. [ML2 T−2] B. Surface Tension II. [ML2 T−1] C. Angular momentum III. [ML−1 T−1] D. Rotational kinetic energy IV. [ML0 T−2] (1) A-II, B-I, C-IV, D-III (2) A-I, B-II, C-III, D-IV (3) A-III, B-IV, C-II, D-I (4) A-IV, B-III, C-II, D-I

Q1. Match List - I with List - II. List - I (Number) List - II (Signficant figure) (A) 1001 (I) 3 (B) 010 . 1 (II) 4 (C) 100 . 100 (III) 5 (D) 0 . 0010010 (IV) 6 Choose the correct answer from the options given below: (1) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (2) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) (3) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (4) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Q1. The angle between vector →Q and the resultant of (2→Q + 2→P) and (2→Q −2→P) is : (1) (2→Q−2 →P) (2) 0∘ tan−1 2→Q+2 →P (3) tan−1(P/Q) (4) tan−1(2Q/P)

Q1. To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is : (1) 5% (2) 1% (3) 3% (4) 4%

Q1. Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit. (1) T 2 = 4π2r2GM (2) T 2 = GM4π2r2 (3) T 2 = 4π2r3GM (4) T 2 = 4π2r3

Q1. If mass is written as 𝑚= 𝑘𝑐𝑃𝐺-1 / 2 ℎ1 / 2, then the value of 𝑃 will be : (Constants have their usual meaning with 𝑘 a dimensionless constant) 1 1 (1) (2) 2 3 (3) 2 (4) -1 3

Q1. A particle moves in x −y plane under the influence of a force →F such that its linear momentum is →p(t) = ^i cos(kt) −^j sin(kt). If k is constant, the angle between →F and →p will be : (1) π (2) π 4 6 (3) π (4) π 2 3

Q1. The resistance R = VI , where V = (200 ± 5) V and I = (20 ± 0. 2) A, the percentage error in the measurement of R is : (1) 3. 5% (2) 7% (3) 3% (4) 5. 5%

Q1. If the percentage errors in measuring the length and the diameter of a wire are 0 . 1% each. The percentage error in measuring its resistance will be: (1) 0 . 2% (2) 0 . 3% (3) 0 . 1% (4) 0 . 144% Q2. 1 𝑏2 A force is represented by 𝐹= 𝑎𝑥2 + 𝑏𝑡 2, where 𝑥= distance and 𝑡= time. The dimensions of are : 𝑎 (1) [𝑀𝐿3 𝑇 – 3 ] (2) [𝑀𝐿𝑇– 2] (3) [𝑀𝐿– 1 𝑇– 1] (4) [𝑀𝐿2 𝑇– 3]

Q1. A physical quantity Q is found to depend on quantities a, b, c by the relation Q = a4b3 . The percentage error in c2 a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is: (1) 66% (2) 43% (3) 34% (4) 14%

Q1. If ϵ0 is the permittivity of free space and E is the electric field, then ϵ0E2 has the dimensions : (1) [M−1 L−3 T4 A2] (2) [ML2 T−2] (3) [M∘L−2TA] (4) [ML−1 T−2]

Q2. A particle is moving in a straight line. The variation of position x as a function of time t is given as x = (t3 −6t2 + 20t + 15) m. The velocity of the body when its acceleration becomes zero is: (1) 4 m s−1 (2) 8 m s−1 (3) 10 m s−1 (4) 6 m s−1

Q2. Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings in correct significant figure is : (1) 5 s (2) 4.623 s (3) 4.6 s (4) 4.62 s

Q2. The angle of projection for a projectile to have same horizontal range and maximum height is : (1) tan−1(4) (2) tan−1 ( 14 ) (3) tan−1 ( 21 ) (4) tan−1(2)

Q2. A body starts moving from rest with constant acceleration covers displacement S1 in first (p −1) seconds and S2 in first p seconds. The displacement S1 + S2 will be made in time : (1) (2p + 1) s (2) √(2p2 −2p + 1) s (3) (2p −1) s (4) (2p2 −2p + 1) s

Q2. A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is: (1) √8 km (2) 8 km (3) 6 km (4) 4 km

Q2. What is the dimensional formula of ab−1 in the equation (P + V2a )(V −b) = RT, where letters have their usual meaning. (1) [M−1 L5 T3] (2) [M6 L7 T4] (3) [ML2 T−2] (4) [M0 L3 T−2]

Q2. A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is : (1) 10 m/s (2) 8 m/s (3) 9.2 m/s (4) 8.8 m/s

Q2. Consider two physical quantities 𝐴 and 𝐵 related to each other as 𝐸= 𝐵−𝑥2 where 𝐸, 𝑥 and 𝑡 have dimensions 𝐴𝑡 of energy, length and time respectively. The dimension of 𝐴𝐵 is (1) 𝐿−2𝑀1𝑇0 (2) 𝐿2𝑀-1𝑇1 (3) 𝐿−2𝑀-1𝑇1 (4) 𝐿0𝑀-1𝑇1

Q2. A particle of mass m projected with a velocity u making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is : (1) √3 mu3 (2) √3 mu2 16 g 2 g (3) mu3 (4) zero √2g

Q2. Projectiles 𝐴 and 𝐵 are thrown at angles of 45° and 60° with vertical respectively from top of a 400 m high tower. If their times of flight are same, the ratio of their speeds of projection 𝑣𝐴: 𝑣𝐵 is: (1) 1: √3 (2) √2: 1 (3) 1: 2 (4) 1: √2

Q2. LIST I LIST II A. Torque I. [M 1L1T −2A−2] Match List I with List II B. Magnetic field II. [L2A1] Choose the correct C. Magnetic moment III. [M 1T −2A−1] D. Permeability of free space IV. [M 1L2T −2] answer from the options given below: (1) A-III, B-I, C-II, D-IV (2) A-IV, B-II, C-III, D-I (3) A-IV, B-III, C-II, D-I (4) A-I, B-III, C-II, D-IV

Q2. Two cars are travelling towards each other at speed of 20 m s−1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s−2 . The distance between them when they come to rest is : (1) 200 m (2) 100 m (3) 50 m (4) 25 m

Q2. A bullet is fired into a fixed target looses one third of its velocity after travelling 4 cm. It penetrates further 𝐷× 10-3 m before coming to rest. The value of 𝐷 is : (1) 32 (2) 5 (3) 3 (4) 4