Practice Questions

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. 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 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 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 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 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 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. 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 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. 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 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 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 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. 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 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. The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is: (1) 1 : 9 (2) 1 : 3 (3) 1 : 27 (4) 1 : 81

Q5. Three bodies A, B and C have equal kinetic energies and their masses are 400 g. 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is : (1) √2; √3; 1 (2) 1 : √3 : 2 (3) 1 : √3 : √2 (4) √3 : √2 : 1

Q5. A body of mass 2 kg begins to move under the action of a time dependent force given by → 𝐹= 6𝑡 ^i + 6𝑡2 ^j N. The power developed by the force at the time 𝑡 is given by: (1) 6𝑡4 + 9𝑡5 W (2) 3𝑡3 + 6𝑡5 W (3) 9𝑡5 + 6𝑡3 W (4) 9𝑡3 + 6𝑡5 W JEE Main 2024 (31 Jan Shift 2) JEE Main Previous Year Paper 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 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 spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m . The impulse of force imparted by the ground to the body is given by: (given g = 9. 8 m s−2 ) (1) 4. 32 kg m s−1 (2) 43. 2 kg m s−1 (3) 23. 9 kg m s−1 (4) 2. 39 kg m s−1 JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper

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 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