Practice Questions

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. 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. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is (1) 192 m (2) 136 m (3) 272 m (4) 68 m

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

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. 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. 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. 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. 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. 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. 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. 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

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. Consider a block kept on an inclined plane (inclined at 45° ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (µ) is equal to : . (1) 0. 33 (2) 0. 60 (3) 0. 25 (4) 0. 50

Q4. A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation v = 10√x m s−1 the force acting on the body is: (1) 125 N (2) 25 N (3) 166 N (4) 5 N

Q4. A body of mass (5 ± 0. 5) kg is moving with a velocity of (20 ± 0. 4) m s−1. Its kinetic energy will be (1) (1000 ± 0. 14) J (2) (500 ± 0. 14) J (3) (500 ± 140) J (4) (1000 ± 140) J

Q4. As per the given figure, a small ball 𝑃 slides down the quadrant of a circle and hits the other ball 𝑄 of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball 𝑄 after collision will be : ( 𝑔 = 10 m s-2 ) (1) 0 (2) 0 . 25 m s-1 (3) 2 m s-1 (4) 4 m s-1

Q4. An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s-1 to keep it in position. The number of bullets fired per second by the machine gun is : (1) 50 (2) 25 (3) 100 (4) 5 𝜌

Q4. Two projectiles A and B are thrown with initial velocities of 40 m s−1 and 60 m s−1 at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is (g = 10 m s−2) (1) 4 : 9 (2) 2 : √3 (3) √3 : 2 (4) 1 : 1 m s−1 . If the force acting on the

Q4. The position vector of a particle related to time t is given by →r= (10tˆi + 15t2ˆj + 7ˆk)m . The direction of net force experienced by the particle is : (1) Positive x-axis (2) In x −y plane (3) Positive y-axis (4) Positive z-axis

Q4. A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, 𝑔 = 10 m s – 2 ): (1) 0 . 60 (2) 0 . 75 (3) 0 . 50 (4) 0 . 25 𝑣𝑒

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

Q4. A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0. 34. [Take g = 10 m s−2 ] (1) 3. 4 m s−1 (2) 22. 4 m s−1 (3) 13 m s−1 (4) 17 m s−1

Q4. A bullet of mass 0. 1 kg moving horizontally with speed 400 m s−1 hits a wooden block of mass 3. 9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is _______. (1) 0. 90 (2) 0. 50 (3) 0. 65 (4) 0. 25

Q4. A mass 𝑚 is attached to two springs as shown in figure. The spring constants of two springs are 𝐾1 and 𝐾2 . For the frictionless surface, the time period of oscillation of mass 𝑚 is (1) 𝑚 (2) 1 K1 - K2 2𝜋√ K1 + K2 2𝜋√ 𝑚 (3) 𝑚 (4) 1 K1 + K2 2𝜋√ K1 - K2 2𝜋√ 𝑚