Practice Questions

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

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. The distance travelled by an object in time 𝑡 is given by 𝑠= 2 . 5𝑡2 . The instantaneous speed of the object at 𝑡= 5 s will be : (1) 25 m s – 1 (2) 5 m s – 1 (3) 62 . 5 m s – 1 (4) 12 . 5 m s – 1

Q3. An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be : (1) 2√gR (2) √gR (3) √gR2 (4) √2gR

Q3. As shown in figure, a 70 kg garden roller is pushed with a force of →𝐹= 200 N at an angle of 30° with horizontal. The normal reaction on the roller is (Given 𝑔= 10 m s-2) (1) 800√2 N (2) 600 N (3) 800 N (4) 200√3 N Q4. 100 balls each of mass 𝑚 moving with speed 𝑣 simultaneously strike a wall normally and reflected back with same speed, in time 𝑡 s. The total force exerted by the balls on the wall is 100𝑚𝑣 200𝑚𝑣 (1) (2) 𝑡 𝑡 (3) 200 𝑚𝑣𝑡 (4) 𝑚𝑣 100𝑡

Q3. As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30° , with horizontal. For μs = 0. 25 , the block will just start to move for the value of F : [Given g = 10 m ⋅s–2 ] (1) 33. 3 N (2) 25. 2 N (3) 20 N (4) 35. 7 N

Q3. An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x = +2 m, its velocity is −4ˆj m s−1 . The object’s velocity (v) and acceleration (a) at x = –2 m will be (1) v = 4ˆi m s−1, a = 8ˆj m s−2 (2) v = 4ˆj m s−1, a = 8ˆi m s−2 (3) v = −4ˆj m s−1, a = 8ˆi m s−2 (4) v = −4ˆi m s−1, a = −8ˆj m s−2

Q3. The trajectory of projectile, projected from the ground is given by y = x −x220 . Where meter. The maximum height attained by the projectile will be. (1) 200 m (2) 10 m (3) 5 m (4) 10√2 m

Q3. A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre: (1) 8 cm (2) 4 cm (3) 1 cm (4) 2 cm

Q3. A passenger sitting in a train A moving at 90 km h-1 observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km h-1, then length of train B is: (1) 120 m (2) 320 m (3) 80 m (4) 200 m

Q3. A ball is thrown vertically upward with an initial velocity of 150 m s−1 . The ratio of velocity after 3 s and 5 s is x+1 . The value of x is _____. {take, g = 10 m s−2 } x (1) 10 (2) −5 (3) 6 (4) 5

Q3. The range of the projectile projected at an angle of 15∘ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45∘ with horizontal, then its range will be (1) 100 m (2) 100√2 m (3) 50√2 m (4) 50 m

Q3. The ratio of powers of two motors is 3√x , that are capable of raising 300 kg water in 5 minutes and 50 kg √x+1 water in 2 minutes respectively from a well of 100 m deep. The value of x will be (1) 16 (2) 2 (3) 2. 4 (4) 4

Q3. A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3. 14 s. The radius of the merry- go-round is 2 m. The centrifugal force on the child will be (1) 80 N (2) 40 N (3) 100 N (4) 50 N

Q3. Two objects are projected with same velocity u however at different angles α and β with the horizontal. If α + β = 90° , the ratio of horizontal range of the first object to the 2nd object will be : (1) 4 : 1 (2) 2 : 1 (3) 1 : 2 (4) 1 : 1

Q3. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N , then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is: (1) 20 m s−1 (2) 40 m s−1 (3) 400 m s−1 (4) 10 m s−1

Q3. A projectile is projected at 30° from horizontal with initial velocity 40 m s−1 . The velocity of the projectile at t = 2 s from the start will be: (1) 40√3 m s−1 (2) Zero (3) 20 m s−1 (4) 20√3 m s−1

Q3. Dimension of 1 should be equal to μ0ε0 (1) L T−1 (2) T2 L−2 (3) L2 T−2 (4) T L−1

Q3. The position of a particle related to time is given by x = (5t2 −4t + 5) m. The magnitude of velocity of the particle at t = 2 s will be : (1) 06 m s−1 (2) 14 m s−1 (3) 10 m s−1 (4) 16 m s−1

Q3. A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 m s – 1 . Neglecting the air resistance, the speed with which the stone hits the ground will be _____ m s – 1 (given, 𝑔 = 10 m s – 2 ). (1) 20 (2) 15 (3) 30 (4) 25

Q3. A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be : (1) 1 : 2 (2) 1 : 4 (3) 4 : 1 (4) 4 : 3

Q3. A car travels a distance of x with speed v1 and then same distance x with speed v2 in the same direction. The average speed of the car is: (1) v1v2 (2) v1+v2 2(v1+v2) 2 (3) 2x (4) 2v1v2 v1+v2 v1+v2

Q4. A body of mass 200 g is tied to a spring of spring constant 12. 5 N m−1 , while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad s−1 , then the ratio of extension in the spring to its natural length will be : (1) 1 : 2 (2) 1 : 1 (3) 2 : 3 (4) 2 : 5 Q5. → + N , where ˆi A body of mass 1 kg begins to move under the action of a time dependent force F = (tˆi 3t2ˆj) and ˆj are the unit vectors along x and y axis. The power developed by above force, at the time t = 2 s , will be _______ W.

Q4. A car is moving with a constant speed of 20 m s−1 in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m s−2 ) (1) π (2) π 6 2 (3) π (4) π 4 3