Practice Questions

Q1. Given below are two statements : Statement (I) : Dimensions of specific heat is [L2 T−2 K−1]. Statement (II) : Dimensions of gas constant is [ML2 T−1 K−1]. In the light of the above statements, choose the most appropriate answer from the options given below. (1) Both statement (I) and statement (II) are correct (2) Statement (I) is correct but statement (II) is incorrect (3) Both statement (I) and statement (II) are incorrect (4) Statement (I) is incorrect but statement (II) is Statement (I) is incorrect but statement (II) is correct correct

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. In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are Δu and Δv , respectively. The error in the measurement of the focal length of the convex lens will be: (1) 2f [ Δuu + Δvv ] (2) Δuu + Δvv (3) f 2 [ Δuu2 + Δvv2 ] (4) f [ Δuu + Δvv ]

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. 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. 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]

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. Given below are two statements: Statement (I) : Planck's constant and angular momentum have the same dimensions. Statement (II) : Linear momentum and moment of force have the same dimensions. In light of the above statements, choose the correct answer from the options given below : (1) Statement I is true but Statement II is false (2) Both Statement I and Statement II are false (3) Both Statement I and Statement II are true (4) Statement I is false but Statement II is true

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. If two vectors →𝐴 and →𝐵 having equal magnitude 𝑅 are inclined at an angle 𝜃, then 𝜃 2𝑅sin (1) →𝐴− →𝐵= √2𝑅sin 𝜃2 (2) →𝐴+ →𝐵= 2 → → 𝜃 → → 𝜃 (3) 𝐴+ 𝐵= 2𝑅cos (4) 𝐴− 𝐵= 2𝑅cos 2 2

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. 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]

Q2. The equation of stationary wave is : y = 2a sin ( 2πntλ ) cos ( 2πxλ ). Which of the following is NOT correct : (1) The dimensions of n/λ is [T] (2) The dimensions of n is [LT−1] (3) The dimensions of x is [L] (4) The dimensions of nt is [L]

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. Train A is moving along two parallel rail tracks towards north with 72 km h-1 and train 𝐵 is moving towards south with speed 108 km h-1. Velocity of train 𝐵 with respect to 𝐴 and velocity of ground with respect to 𝐵 are (in m s-1): (1) -30 and 50 (2) -50 and -30 (3) -50 and 30 (4) 50 and -30

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. 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

Q2. Position of an ant ( S in metres) moving in Y −Z plane is given by S = 2t2ˆj + 5ˆk (where t is in second). The magnitude and direction of velocity of the ant at t = 1 s will be : (1) 16 m s−1 in y-direction (2) 4 m s−1 in x-direction (3) 9 m s−1 in z-direction (4) 4 m s−1 in y-direction

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. 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 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 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. 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. Young's modulus is determined by the equation given by Y = 49000 ml cm2dyn where M is the mass and l is the extension of wire used in the experiment. Now error in Young modules (Y ) is estimated by taking data from M −l plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is : (1) 0.5% (2) 2% (3) 0.02% (4) 0.2%