Practice Questions

Q2. A particle of mass m projected with a velocity u making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is : (1) √3 mu3 (2) √3 mu2 16 g 2 g (3) mu3 (4) zero √2g

Q2. Projectiles 𝐴 and 𝐵 are thrown at angles of 45° and 60° with vertical respectively from top of a 400 m high tower. If their times of flight are same, the ratio of their speeds of projection 𝑣𝐴: 𝑣𝐵 is: (1) 1: √3 (2) √2: 1 (3) 1: 2 (4) 1: √2

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. 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

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 man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is ( in m/s2 ) : (1) 57600π2 ms−2 (2) Zero (3) 4π2 ms−2 (4) 16π2 ms−2

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 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 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. Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Statement I is correct but Statement II is incorrect (2) Statement I is incorrect but Statement II is correct (3) Both Statement I and Statement II are incorrect (4) Both Statement I and Statement II are correct

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 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. The relation between time ‘𝑡’ and distance ‘𝑥’ is 𝑡= 𝛼𝑥2 + 𝛽𝑥, where 𝛼 and 𝛽 are constants. The relation between acceleration 𝑎 and velocity 𝑣 is: (1) 𝑎= - 2𝛼𝑣3 (2) 𝑎= - 5𝛼𝑣5 (3) 𝑎= - 3𝛼𝑣2 (4) 𝑎= - 4𝛼𝑣4

Q3. A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t , then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h ) : (1) 40 (2) 80 (3) 30 (4) 70

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 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. A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take π = 3.14 ) : (1) 140.5 (2) 118.9 (3) 139.4 (4) 220.0

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

Q4. A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If →𝐹1 is the force required to → just move the block up the inclined plane and 𝐹2 is the force required to just prevent the block from sliding down, then the value of →𝐹1 − →𝐹2 is: [Use 𝑔= 10 m s-2] (1) 25√3 N (2) 5√3 N (3) 5√3 N (4) 10 N 2

Q4. A satellite of 103 kg mass is revolving in circular orbit of radius 2R. If 104R6 it would revolve in a new circular orbit of radius (use g = 10 m/s2, R = radius of earth) (1) 2.5R (2) 3R (3) 4R (4) 6R

Q4. A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2 > m1 ). If the acceleration of the system is g , then the ratio of the masses m1 is: √2 m2 (1) 1+√5 (2) √2−1 √5−1 √2+1 (3) 1+√5 (4) √3+1 √2−1 √2−1

Q4. The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m . If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g = 10 m s−2 ] (1) 6√5 m s−1 (2) 5√6 m s−1 (3) 5√5 m s−1 (4) 2√5 m s−1

Q4. A block of mass 𝑚 is placed on a surface having vertical cross section given by 𝑦= 𝑥2 . If coefficient of friction 4 is 0 . 5, the maximum height above the ground at which block can be placed without slipping is: 1 1 (1) m (2) m 4 2 (3) 1 m (4) 1 m 6 3

Q4. A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = α√x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be : (1) m (2) md 2α2 d 2α2 (3) 2 mα2 d (4) mα22 d

Q4. A body of m kg slides from rest along the curve of vertical circle from point A to B in friction less path. The velocity of the body at B is: (given, R = 14 m, g = 10 m/s2 and √2 = 1.4 ) (1) 16.7 m/s (2) 19.8 m/s (3) 10.6 m/s (4) 21.9 m/s