Practice Questions

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 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. 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. 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 ]

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 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. 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 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. 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

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

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

Q3. If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the √uG : (1) pressure gradient per unit mass (2) Gravitational potential (3) Energy per unit mass (4) Force per unit mass

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,

Q3. A 2 kg brick begins to slide over a surface which is inclined at an angle of 45∘ with respect to horizontal axis. The co-efficient of static friction between their surfaces is: (1) 1.7 (2) 1 √3 (3) 0.5 (4) 1

Q3. Three blocks 𝐴, 𝐵 and 𝐶 are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions 𝑇1 and 𝑇2 in the string are respectively: (1) 40N, 64N (2) 60N, 80N (3) 88N, 96N (4) 80N, 100N

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

Q3. A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if π2 = 9. 8 and g = 9. 8 m s−2 ) (1) 97 N (2) 9. 8 N (3) 8. 82 N (4) 17. 8 N

Q3. A train is moving with a speed of 12 m s−1 on rails which are 1. 5 m apart. To negotiate a curve radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g = 10 m s−2 ): (1) 6. 0 cm (2) 5. 4 cm (3) 4. 8 cm (4) 4. 2 cm

Q3. All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is: (1) g (2) g 3 (3) g (4) g 2 4

Q3. A given object takes n times the time to slide down 45∘ rough inclined plane as it takes the time to slide down an identical perfectly smooth 45∘ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is : (1) √1 − n21 (2) 1 −n2 (3) 1 − 1 (4) √1 −n2 n2

Q3. A particle moving in a circle of radius 𝑅 with uniform speed takes time 𝑇 to complete one revolution. If this particle is projected with the same speed at an angle 𝜃 to the horizontal, the maximum height attained by it is equal to 4𝑅. The angle of projection 𝜃 is then given by : (1) 12 (2) 𝜋2𝑅 12 sin−12𝑔𝑇2 sin−1 𝜋2𝑅 2𝑔𝑇2 (3) 12 (4) 𝜋𝑅 12 cos−12𝑔𝑇2 cos−1 𝜋2𝑅 2𝑔𝑇2

Q3. A body travels 102.5 m in nth second and 115.0 m in (n + 2)th second. The acceleration is : (1) 6.25 m/s2 (2) 12.5 m/s2 (3) 9 m/s2 (4) 5 m/s2

Q3. If the radius of curvature of the path of two particles of same mass are in the ratio 3 : 4, then in order to have constant centripetal force, their velocities will be in the ratio of: (1) √3 : 2 (2) 1 : √3 (3) √3 : 1 (4) 2 : √3