Practice Questions

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 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,

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 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 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. 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 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 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. 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 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 particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is: (Take g = 10 m s−2). (1) 20 m s−1 (2) √10 m s−1 (3) 2√10 m s−1 (4) 10 m s−1

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

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 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 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. A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ( θ ) of thread deflection in the extreme position will be : (1) tan-1 ( √2 ) (2) 2tan-112 (3) tan-11 (4) 2tan-1 1 2 √5

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 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 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 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 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. 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 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