Practice Questions

Q50.The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, $\mathrm{n}=_________ Consider all the bodies have equal masses.

Q61.Given below are two statements about X-ray spectra of elements : Statement (I) : A plot of √v ( v = frequency of X -rays emitted) vs atomic mass is a straight line. Statement (II) : A plot of v(v = frequency of X -rays emitted) vs atomic number is a straight line. In the light of the above statements, choose the correct answer from the options given below : (1) Both Statement I and Statement II are true (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Statement I is true but Statement II is false

Q62.If a0 is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer] (1) 8πa0 (2) 2a0 n nπ (3) 4n (4) 4πa0 πa0 n

Q68.Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H atom is suitable for this? Given : Rydberg constant RH = 105 cm−1, h = 6.6 × 10−34 J s, c = 3 × 108 m/s ) (1) Balmer series, ∞→2 (2) Lyman series, ∞→1 (3) Paschen series, ∞→3 (4) Paschen series, 5 →3

Q68.Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K . If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following (1) Volume of system increases . (2) The solid phase (ice) disappears completely. (3) Liquid phase disappears completely. (4) The amount of ice decreases.

Q1. The radius 𝑟, length 𝑙 and resistance 𝑅 of a metal wire was measured in the laboratory as 𝑟= 0 .35 ± 0 .05 cm, 𝑅= 100 ± 10 ohm, 𝑙= 15 ± 0 .2 cm The percentage error in resistivity of the material of the wire is : (1) 25 . 6% (2) 39 .9 % (3) 37 . 3% (4) 35 .6 %

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. 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. 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. 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%

Q2. A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1 . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t2 . Time required to reach the ground, if it is dropped from the top of the tower, is : (1) √t1t2 (2) √t1 + t2 (3) √t1 −t2 (4) √t1t2

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. 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. 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. 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. 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. 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. 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%

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. 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. 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

Q3. The relation between time ‘𝑡’ and distance ‘𝑥’ is 𝑡= 𝛼𝑥2 + 𝛽𝑥, where 𝛼 and 𝛽 are constants. The relation between acceleration 𝑎 and velocity 𝑣 is: (1) 𝑎= - 2𝛼𝑣3 (2) 𝑎= - 5𝛼𝑣5 (3) 𝑎= - 3𝛼𝑣2 (4) 𝑎= - 4𝛼𝑣4

Q3. A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' F ' is applied at the mid point of the rope so that the rope makes an angle of 45∘ with respect to the vertical axis as shown in figure. The magnitude of F is : (Assume that the system is in equilibrium and g = 10 m/s2 ) (1) 10 N (2) 10 N √2 (3) 1 N (4) 1 N 10×√2 J energy is supplied to the satellite,