Practice Questions

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 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. 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 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 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. 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. 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. 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 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 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 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 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

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

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 co-ordinates of a particle moving in x −y plane are given by : x = 2 + 4t, y = 3t + 8t2 . The motion of the particle is : (1) uniformly accelerated having motion along a (2) uniform motion along a straight line. parabolic path. (3) uniformly accelerated having motion along a (4) non-uniformly accelerated. straight line.

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 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 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 small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball? (1) (2) (3) (4)

Q4. Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0 . 04, the acceleration of the system in m s-2 is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) : (1) 3 (2) 4 (3) 2 (4) 1 . 2

Q4. A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of 0.1 ms−2 . The action force of the system on the floor is equal to: (1) 196 N (2) 291 N (3) 294 N (4) 297 N

Q5. In the given arrangement of a doubly inclined plane two blocks of masses 𝑀 and 𝑚 are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0 . 25. The value of 𝑚, for which 𝑀= 10 kg will move down with an 3 acceleration of 2 m s-2, is: (take 𝑔= 10 m s-2 and tan 37° = 4) (1) 9 kg (2) 4 . 5 kg (3) 6 . 5 kg (4) 2 . 25 kg

Q5. A bob of mass m is suspended by a light string of length L. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies ( K.E. )A is : ( K.E. )B (1) 3 : 2 (2) 5 : 1 (3) 2 : 5 (4) 1 : 5