Practice Questions

Q1. A person travels 𝑥 distance with velocity 𝑣1 and then 𝑥 distance with velocity 𝑣2 in the same direction. The average velocity of the person is 𝑣, then the relation between 𝑣, 𝑣1 and 𝑣2 will be 𝑣1 + 𝑣2 1 1 1 (1) 𝑣= (2) 𝑣= 𝑣1 + 𝑣2 2 2 1 1 (3) 𝑣= 𝑣1 + 𝑣2 (4) 𝑣= 𝑣1 + 𝑣2

Q1. If 𝑅, 𝑋𝐿 and 𝑋𝐶 represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: 𝑅 (1) 𝑅 𝑋𝐿 𝑋𝐶 (2) √𝑋𝐿𝑋𝑐 𝑅 𝑋𝐿 (3) (4) 𝑅 𝑋𝐿𝑋𝑐 𝑋𝑐

Q1. Two trains A and B of length l and 4l are travelling into a tunnel of length L in parallel tracks from opposite directions with velocities 108 km h−1 and 72 km h−1, respectively. If train A take 35 s less time than train B to cross the tunnel then, length L of tunnel is: (Given L = 60 l) (1) 1200 m (2) 900 m (3) 1800 m (4) 2700 m

Q1. If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is: 2 c 2 G1] (2) h1c1G−1 (1) [h 1 1 2 c 2 G 2 ] (4) [h 2 c 2 G−12 ] (3) [h−1 1 1 1 1

Q1. When vector A = 2ˆi + 3ˆj + 2ˆk is subtracted from vector B, it gives a vector equal to 2ˆj. Then the magnitude of → vector B will be: (1) √5 (2) 3 (3) √6 (4) √33

Q1. Match List I with List II List I List II A Torque I kg m–1 s–2 B Energy density II kg m s–1 C Pressure gradient III kg m–2 s–2 D Impulse IV kg m2 s–2 Choose the correct answer from the options given below : (1) A-IV, B-III, C-I, D-II (2) A-I, B-IV, C-III, D-II (3) A-IV, B-I, C-II, D-III (4) A-IV, B-I, C-III, D-II

Q1. A vector in x −y plane makes an angle of 30o with y -axis. The magnitude of y -component of vector is 2√3. The magnitude of x-component of the vector will be : (1) 1 (2) 6 √3 (3) 2 (4) √3

Q1. Match List I with List II : List-I (Physical Quantity) List-II (Dimensional Formula) A Pressure gradient I [M0L2T−2] B Energy density II [M1L−1T−2] C Electric Field III [M1L−2T−2] D Latent heat IV [M1L1T−3A−1] Choose the correct answer from the options given below: (1) A-III, B-II, C-I, D-IV (2) A-II, B-III, C-IV, D-I (3) A-III, B-II, C-IV, D-I (4) A-II, B-III, C-I, D-IV

Q1. Three forces F1 = 10 N, F2 = 8 N, F3 = 6 N are acting on a particle of mass 5 kg. The forces F2 and F3 are applied perpendicularly so that particle remains at rest. If the force F1 is removed, then the acceleration of the particle is (1) 7 m s–2 (2) 0. 5 m s–2 (3) 4. 8 m s–2 (4) 2 m s–2

Q1. In the equation 𝑋+ 𝑎 𝑏] = 𝑅𝑇, 𝑋 is pressure, 𝑌 is volume, 𝑅 is universal gas constant and 𝑇 is 𝑌2[𝑌- temperature. The physical quantity equivalent to the ratio 𝑎 is: 𝑏 (1) Pressure gradient (2) Energy (3) Impulse (4) Coefficient of viscosity

Q1. Match List I with List II List I List II A. Torque I. M L−2 T−2 B. Stress II. M L2 T−2 C. Pressure gradient III. M L−1 T−1 Coefficient of D. IV. M L−1 T−2 viscosity Choose the correct answer from the options given below : (1) A-II, B-I, C-IV, D-III (2) A-IV, B-II, C-III, D-I (3) A-II, B-IV, C-I, D-III (4) A-III, B-IV, C-I, D-II

Q2. A particle is moving with constant speed in a circular path. When the particle turns by an angle 90°, the ratio of instantaneous velocity to its average velocity is 𝜋: 𝑥√2 . The value of 𝑥 will be (1) 2 (2) 5 (3) 1 (4) 7

Q2. A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is (1) 2R (2) R√(π2 + 4) (3) R√(π2 + 1) (4) 2R√(1 + 4π2)

Q2. The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as: ν = raρbsc . The values of a, b and c respectively are (1) (−32 , −12 , 12 ) (2) (−32 , 12 , 12 ) (3) ( 23 , 12 , −12 ) (4) ( 32 , −12 , 12 )

Q2. An object moves with speed 𝑣1, 𝑣2 and 𝑣3 along a line segment 𝐴𝐵, 𝐵𝐶 and 𝐶𝐷 respectively as shown in figure. Where 𝐴𝐵 = 𝐵𝐶 and 𝐴𝐷 = 3 𝐴𝐵, then average speed of the object will be : (1) 𝑣1 + 𝑣2 + 𝑣3 (2) 𝑣1𝑣2𝑣3 3 3𝑣1𝑣2 + 𝑣2𝑣3 + 𝑣3𝑣1 3𝑣1𝑣2𝑣3 𝑣1 + 𝑣2 + 𝑣3 (3) (4) 𝑣1𝑣2 + 𝑣2𝑣3 + 𝑣3𝑣1 3𝑣1𝑣2𝑣3

Q2. Match List I with List II List-I List-II A Spring constant I [T –1] B Angular speed II [MT –2] C Angular momentum III [ML2] D Moment of Inertia IV [ML2T –1] Choose the correct answer from the options given below: (1) A-I, B-III, C-II, D-IV (2) A-IV, B-I, C-III, D-II (3) A-II, B-I, C-IV, D-III (4) A-II, B-III, C-I, D-IV

Q2. As shown in the figure, a particle is moving with constant speed π m s−1 . Considering its motion from A to B, the magnitude of the average velocity is: (1) √3 m s−1 (2) π m s−1 (3) 1. 5√3 m s−1 (4) 2√3 m s−1

Q2. Match List I with List II List - I List - II A Surface tension I. kg m−1 s−1 B Pressure II. kg m s−1 C Viscosity III. kg m−1 s−2 D Impulse IV. kg s−2 Choose the correct answer from the options given below: (1) A-IV, B-III, C-II, D-I (2) A-IV, B-III, C-I, D-II (3) A-III, B-IV, C-I, D-II (4) A-II, B-I, C-III, D-IV

Q2. The equation of a circle is given by x2 + y2 = a2 , where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : (x −At)2 + (y − Bt ) 2 = a2 The dimensions of t is given as [T−1] (1) A = [L–1T], B = [LT–1] (2) A = [LT], B = [L–1T –1] (3) A = [L–1T –1 ], B = [LT–1] (4) A = [L–1T –1], B = [LT]

Q2. A vehicle travels 4 km with speed of 3 km h−1 and another 4 km with speed of 5 km h−1 , then its average speed is : (1) 4. 25 km h−1 (2) 3. 50 km h−1 (3) 4. 00 km h−1 (4) 3. 75 km h−1

Q2. The speed of a wave produced in water is given by ν = λagbρc . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are (1) 1, −1, 0 (2) 12 , 0, 12 (3) 1, 1, 0 (4) 21 , 12 , 0

Q2. If force (F), velocity (V ) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be : (1) F V 4 T −6 (2) F V −4 T −2 (3) F 2 V −2 T 6 (4) F V −2 T 2

Q2. The initial speed of a projectile fired from ground is 𝑢. At the highest point during its motion, the speed of √3 projectile is 𝑢. The time of flight of the projectile is: 2 (1) 𝑢 (2) 𝑢 2𝑔 𝑔 2𝑢 √3𝑢 (3) (4) 𝑔 𝑔

Q2. The distance travelled by a particle is related to time t as x = 4t2 . The velocity of the particle at t = 5 s is (1) 40 m s–1 (2) 25 m s–1 (3) 20 m s–1 (4) 8 m s–1

Q2. Match List I with List II List I List II A Angular momentum I [ML2 T−2] B Torque II [ML−2 T−2] C Stress III [ML2 T−1] D Pressure gradient IV [ML−1 T−2] Choose the correct answer from the options given below : (1) A-I, B-IV, C-III, D-II (2) A-III, B-I, C-IV, D-II (3) A-II, B-III, C-IV, D-I (4) A-IV, B-II, C-I, D-III