Practice Questions

Q1. The distance of the Sun from earth is 1. 5 × 1011 m and its angular diameter is 2000′′ when observed from the earth. The diameter of the Sun will be (1) 2. 45 × 1010 m (2) 1. 45 × 1010 m (3) 1. 45 × 109 m (4) 0. 14 × 109 m

Q1. If 𝑍= 𝐴2𝐵3 , then the relative error in 𝑍 will be 𝐶4 2𝛥𝐴 3𝛥𝐵 4𝛥𝐶 𝛥𝐴 𝛥𝐵 𝛥𝐶 (1) 𝐴+ 𝐵+ 𝐶 (2) 𝐴+ 𝐵+ 𝐶 (3) 2𝛥𝐴 3𝛥𝐵 4𝛥𝐶 (4) 𝛥𝐴 𝛥𝐵 𝛥𝐶 𝐴+ 𝐵- 𝐶 𝐴+ 𝐵- 𝐶 Q2. →𝐴 is a vector quantity such that →𝐴= non-zero constant. Which of the following expression is true for →𝐴? (1) →𝐴· →𝐴= 0 (2) →𝐴× →𝐴< 0 (3) →𝐴× →𝐴= 0 (4) →𝐴× →𝐴> 0

Q1. A person moved from 𝐴 to 𝐵 on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given cos135° = - 0 . 7) (1) 42 m (2) 47 m (3) 19 m (4) 40 m

Q1. A silver wire has a mass (0. 6 ± 0. 006)g , radius (0. 5 ± 0. 005) mm and length (4 ± 0. 04) cm . The maximum percentage error in the measurement of its density will be (1) 7% (2) 3% (3) 4% (4) 6%

Q1. Two projectile thrown at 30° and 45° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is (1) 1 : √2 (2) 2 : 1 (3) √2 : 1 (4) 1 : 2

Q2. A projectile is projected with velocity of 25 m s−1 at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be : [use use g = 10 m s−2 ] (1) 1 5t2 (2) 1 4R 2 sin−1( 4R ) 2 sin−1( 5t2 ) (3) tan−1( 4t25R ) (4) cot−1( 20t2R )

Q2. Motion of a particle in x −y plane is described by a set of following equations x = 4 sin( π2 −ωt) m and y = 4 sin(ωt) m. The path of the particle will be (1) circular (2) helical (3) parabolic (4) eliptical

Q2. Two masses 𝑀1 and 𝑀2 are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass 𝑀2 is twice that of 𝑀1. the acceleration of the system is 𝑎1. When the mass 𝑎1 𝑀2 is thrice that of 𝑀1. The acceleration of The system is 𝑎2. The ratio will be 𝑎2 (1) 1 (2) 2 3 3 3 1 (3) (4) 2 2

Q2. A ball is spun with angular acceleration α = 6t2 −2t where t is in second and α is in rad s−2 . At t = 0, the ball has angular velocity of 10 rad s−1 and angular position of 4 rad . The most appropriate expression for the angular position of the ball is (1) 3 t4 −t2 + 10t (2) t4 2 2 −t33 + 10t + 4 (3) 2t4 3 −t36 + 10t + 12 (4) 2t4 −t32 + 5t + 4

Q2. A NCC parade is going at a uniform speed of 9 km h-1 under a mango tree on which a monkey is sitting at a height of 19 . 6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given 𝑔= 9 . 8 m s-2) (1) 5 m (2) 10 m (3) 19 . 8 m (4) 24 . 5 m

Q2. A projectile is launched at an angle α with the horizontal with a velocity 20 m s−1 . After 10 s , its inclination with horizontal is β . The value of tan β will be : (g = 10 m s−2) . (1) tan α + 5 sec α (2) tan α −5 sec α (3) 2 tan α −5 sec α (4) 2 tan α + 5 sec α

Q2. A person can throw a ball upto a maximum range of 100 m . How high above the ground he can throw the same ball? (1) 25 m (2) 50 m (3) 100 m (4) 200 m

Q2. In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement? (1) 4a1 + 2a2 + a3 + a4 = 0 (2) a1 + 4a2 + 3a3 + a4 = 0 (3) a1 + 4a2 + 3a3 + 2a4 = 0 (4) 2a1 + 2a2 + 3a3 + a4 = 0

Q2. A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height h while going up and coming down respectively. 3 (1) √2−1 (2) √3−√2 √2+1 √3+√2 (3) √3−1 (4) 1 √3+1 3

Q2. The SI unit of a physical quantity is Pascal ‐ sec. The dimensional formula of this quantity will be (1) ML2T −1 (2) M −1L3T 0 (3) ML−1T −1 (4) ML−1T −2

Q2. In van dar Wall equation [P ][V T is temperature. The ratio of constants ab is dimensionally equal to : (1) P (2) V V P (3) PV (4) PV 3

Q2. At time t = 0 a particle starts travelling from a height 7ˆz cm in a plane keeping z coordinate constant. At any instant of time, it's position along the x and y directions are defined as 3t and 5t3 respectively. At t = 1 s acceleration of the particle will be (1) −30y (2) 30y (3) 3x + 15y (4) 3x + 15y + 7ˆz

Q2. A ball is projected from the ground with a speed 15 m s−1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to (1) 1 (2) 1 4 2 (3) 2 (4) 4

Q2. An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 m s−2 ]. (1) 1 : 1 (2) √2 : √3 (3) √3 : √2 (4) 2 : 3

Q2. If momentum 𝑃, area 𝐴 and time 𝑇 are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is (1) PA-1T0 (2) PAT-1 (3) PA-1T (4) PA-1T-1

Q2. Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 ms−2 . The value of F is (Take g = 10 ms−2 ) (1) 3360 N (2) 3380 N (3) 3120N (4) 3240N

Q2. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws 𝑛 balls per second, the maximum height the balls can reach is 𝑔 𝑔 (1) (2) 2𝑛 𝑛 (3) 2𝑔𝑛 (4) 𝑔 2𝑛2

Q3. Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity u at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of u in m s−1 . [use g = 10 m s−2 ] (1) 10 (2) 15 (3) 20 (4) 30

Q3. A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum speed with which the stone can revolve is K π rev min−1 . The value of K is : (Assume the string is massless and un-stretchable) (1) 400 (2) 300 (3) 600 (4) 800

Q3. A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0. 02 . The acceleration of block is: (Given g = 10 m s−2 .) (1) 8 m s−2 (2) 1 m s−2 11 (3) 5 1 m s−2 (4) 54 m s−2