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. 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. 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. 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 %

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. 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. 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 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. 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 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. 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 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. 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 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 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. 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. 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. 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. 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. 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. 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. 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. The dimensional formula of angular impulse is : (1) [M L – 2T – 1] (2) [M L2 T – 2 ] (3) [M L T – 1 ] (4) [M L2 T – 1 ]

Q3. A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take π = 3.14 ) : (1) 140.5 (2) 118.9 (3) 139.4 (4) 220.0

Q3. A light string passing over a smooth light fixed pulley connects two blocks of masses 𝑚1 and 𝑚2. If the 𝑔 acceleration of the system is 8, then the ratio of masses is (1) 9 (2) 8 7 1 4 5 (3) (4) 3 3