Practice Questions

Q4. A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30∘ . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: = 10 m/s2, √3 = 1.73) (g (1) 264 m/s (2) 51.4 m/s (3) 70.4 m/s (4) 102.8 m/s

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. 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. 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. 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

Q4. A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0. 4 , then the work done against friction (in J) is: (1) 4200 (2) 3900 (3) 4000 (4) 4500

Q4. A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is : (1) 1.47 N (2) 147 N (3) 14.7 N (4) 1470 N

Q4. A stationary particle breaks into two parts of masses mA and mB which move with velocities vA and vB respectively. The ratio of their kinetic energies (KB : KA) is : (1) vB : vA (2) mB : mA (3) mBvB : mAvA (4) 1 : 1

Q4. Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is : (1) 3 : 5 (2) 5 : 4 (3) 2 : 5 (4) 4 : 5

Q4. A body of mass 4 kg experiences two forces →𝐹1 = 5 ^𝑖+ 8 ^𝑗+ 7 ^𝑘 and →𝐹2 = 3 ^𝑖- 4 ^𝑗- 3 ^𝑘. The acceleration acting on the body is: (1) -2 ^𝑖- ^𝑗- ^𝑘 (2) 4 ^𝑖+ 2 ^𝑗+ 2 ^𝑘 (3) 2 ^𝑖+ ^𝑗+ ^𝑘 (4) 2 ^𝑖+ 3 ^𝑗+ 3 ^𝑘

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 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 thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is : (1) 3 ω (2) 5 ω 2 4 (3) 2 ω (4) 4 ω 3 5

Q5. A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the normal force applied by the man on bar is: (1) 6 kg - wt (2) 12 kg - wt (3) 3 kg - wt (4) 6√3 kg - wt

Q5. A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10-2 kg moving with a speed of 2 × 102 m s-1. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use 𝑔= 10 m s-2) (1) 0 . 30 m (2) 0 . 20 m (3) 0 . 35 m (4) 0 . 40 m

Q5. A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is : (1) W cos θ (2) W2 (3) W (4) W sin θ

Q5. A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60° by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is : 𝑔= 10 m s-2 (1) 5√3 J (2) 5 J (3) 5 × 103 J (4) 10 J

Q5. A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of : ( R = Radius of earth, g = 10 m s−2 ) (1) 100 N (2) 300 N (3) 225 N (4) 120 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

Q5. When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be: (1) 6% (2) 600% (3) 60% (4) 500%

Q5. A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : (1) 1 : 2 (2) √3 : 2 (3) 2 : 1 (4) 1 : 1

Q5. A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is : (1) √6 m (2) √5 m (3) 1 m (4) 2 m

Q5. A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is : (1) 84% (2) 16% (3) 32% (4) 44%

Q5. A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to : (1) t (2) t3/2 (3) t2 (4) t2/3