Practice Questions

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 light string passing over a smooth light fixed pulley connects two blocks of masses 𝑚1 and 𝑚2. If the 𝑔 acceleration of the system is 8, then the ratio of masses is (1) 9 (2) 8 7 1 4 5 (3) (4) 3 3

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. 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. 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

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 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. 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. 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 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 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. 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. 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 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 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 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 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. 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

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