Practice Questions

Q2. The SI unit of a physical quantity is Pascal ‐ sec. The dimensional formula of this quantity will be (1) ML2T −1 (2) M −1L3T 0 (3) ML−1T −1 (4) ML−1T −2

Q2. At time t = 0 a particle starts travelling from a height 7ˆz cm in a plane keeping z coordinate constant. At any instant of time, it's position along the x and y directions are defined as 3t and 5t3 respectively. At t = 1 s acceleration of the particle will be (1) −30y (2) 30y (3) 3x + 15y (4) 3x + 15y + 7ˆz

Q2. Motion of a particle in x −y plane is described by a set of following equations x = 4 sin( π2 −ωt) m and y = 4 sin(ωt) m. The path of the particle will be (1) circular (2) helical (3) parabolic (4) eliptical

Q2. A NCC parade is going at a uniform speed of 9 km h-1 under a mango tree on which a monkey is sitting at a height of 19 . 6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given 𝑔= 9 . 8 m s-2) (1) 5 m (2) 10 m (3) 19 . 8 m (4) 24 . 5 m

Q2. A person is standing in an elevator. In which situation, he experiences weight loss ? (1) When the elevator moves upward with constant (2) When the elevator moves downward with acceleration constant acceleration (3) When the elevator moves upward with uniform (4) When the elevator moves downward with uniform velocity velocity

Q2. A ball is projected from the ground with a speed 15 m s−1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to (1) 1 (2) 1 4 2 (3) 2 (4) 4

Q3. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ? (1) Momentum (2) Potential energy (3) Acceleration (4) Force

Q3. A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N . If monkey initially climbs down with an acceleration of 4 m s−2 and then climbs up with an acceleration of 5 m s−2 . Choose the correct option (g = 10 m s−2) (1) T = 700 N while climbing upward (2) T = 350 N while going downward (3) Rope will break while climbing upward (4) Rope will break while going downward

Q3. Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding to figure a, b, c and d respectively. (1) W3 > W2 > W1 > W4 (2) W3 > W2 > W4 > W1 (3) W2 > W3 > W4 > W1 (4) W2 > W3 > W1 > W4

Q3. A disc with a flat small bottom beaker placed on it at a distance 𝑅 from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity 𝜔. The coefficient of static friction between the bottom of the beaker and the surface of the disc is 𝜇. The beaker will revolve with the disc if : (1) 𝑅≤𝜇𝑔 (2) 𝑅≤𝜇𝑔 2𝜔2 𝜔2 𝜇𝑔 𝜇𝑔 (3) 𝑅≥ (4) 𝑅≥ 2𝜔2 𝜔2

Q3. If t = √x + 4, then ( dxdt )t=4 is: (1) 4 (2) Zero (3) 8 (4) 16

Q4. A ball is projected with kinetic energy E , at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become : (1) Zero (2) E 2 (3) E (4) E 4

Q4. A block of mass 10 kg starts sliding on a surface with an initial velocity of 9. 8 ms−1 . The coefficient of friction between the surface and block is 0. 5 . The distance covered by the block before coming to rest is :[use g = 9. 8 ms−2 ] (1) 9. 8 m (2) 4. 9 m (3) 12. 5 m (4) 19. 6 m →Q5. + x −y plane. Assume distance in A particle experiences a variable force F = (4xˆi 3y2ˆj) in a horizontal meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x −y plane, then Kinetic Energy changes by : (1) 25 J (2) 50 J (3) 12. 5 J (4) 0 J

Q4. If force →F = 3 ^𝑖+ 4 ^𝑗- 2 ^𝑘 acts on a particle having position vector 2 ^𝑖+ ^𝑗+ 2 ^𝑘 then, the torque about the origin will be: (1) -10 ^i + 10 ^j + 5 ^k (2) 3 ^i + 4 ^j - 2 ^k (3) 10 ^i + 5 ^j - 10 ^k (4) 10 ^i + ^j - 5 ^k

Q4. In two different experiments, an object of mass 5 kg moving with a speed of 25 ms-1 hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following : (1) Impulse and average force acting on the object (2) Impulse will be same for both the cases but the will be same for both the cases. average force will be different. (3) Average force will be same for both the cases but (4) Average force and impulse will be different for the impulse will be different. both the cases.

Q4. A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is (1) 1 (2) 2 5 5 (3) 2 (4) 7 7 10

Q4. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be (1) 1: 1 (2) 2: 1 (3) 1: 4 (4) 4: 1

Q5. Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB . These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits? (1) 2r2A = r3B (2) r3A = 2r3B (3) r3A = 4r3B (4) T A2 −T B2 = GMπ2 (r3B −4r3A)

Q5. The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be (Radius of earth = 6400 km) (1) 1% (2) 3% (3) 4% (4) 0. 5%

Q5. In the given figure, the block of mass m is dropped from the point ′A′ . The expression for kinetic energy of block when it reaches point ′B′ is (1) mgy0 (2) 12 mgy20 (3) 1 mgy2 (4) mg(y −y0) 2

Q5. Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is (1) 4 cm towards the 10 kg block (2) 2 cm away from the 10 kg block (3) 2 cm towards the 10 kg block (4) 4 cm away from the 10 kg block

Q5. The height of any point 𝑃 above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point 𝑃 will be : (Given 𝑔= acceleration due to gravity at the surface of earth). (1) 𝑔 (2) 𝑔 2 4 𝑔 𝑔 (3) (4) 3 9

Q5. If momentum of a body is increased by 20%, then its kinetic energy increases by : (1) 36% (2) 40% (3) 44% (4) 48%

Q6. The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by (Given R = radius of earth) (1) (2) (3) (4)

Q6. The terminal velocity 𝑣𝑡 of the spherical rain drop depends on the radius 𝑟 of the spherical rain drop as (1) 𝑟 (2) 𝑟2 1 1 (3) (4) 𝑟 𝑟2