AjneeshFlame Institute - Part 16

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Page 16

The moment of inertia of a meter scale of mass 0.6 kg about an axis perpendicular to the scale and located at the 20 cm position on the scale in kg m square is (Breadth of the scale is negligible)

(a) 0.074 (b) 0.104 (c) 0.148 (d) 0.208 Ans. b (6)

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A circular disc of radius R and thickness R/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

(a) I (b) 2I/8 (c) I/5 (d) I/10 Ans. c (5)

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A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is (assume that the cube does not slide)

(a) mg/4 (b) 2mg/3 (c) 3mg/4 (d) mg Ans. b (3)

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38. Weights of 1g,2g,……..100g are suspended from the 1 cm, 2 cm, …… 100 cm, marks respectively of a light metre scale. Where should it be supported for the system to be in equilibrium

(a) 55 cm mark (b) 60 cm mark (c) 66 cm mark (d) 72 cm mark Ans. c (27)

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37. A person supports a book between his finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of

(a) w. a/2 anticlockwise (b) w. b/2 anticlockwise (c) wa anticlockwise (d) wa clockwise Ans. b (76)

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36. When a force of 6.0 N is exerted at 30 degree to a wrench at a distance of 8 cm from the nut, it is just able to loosen the nut. What force F would be sufficient to loosen it, if it acts perpendicularly to the wrench at 16 cm from the nut

(a) 3 N (b) 6 N (c) 4 N (d) 1.5 N Ans. d (5)

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A cubical block of side L rests on a rough horizontal surface with coefficient of friction μ . A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

(a) Infinitesimal (b) mg/4 (c) mg/2 (d) mg(1-μ) Ans. c (8)

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33. Two men are carrying a uniform bar of length L , on their shoulders. The bar is held horizontally such that younger man gets (1/4)th load. Suppose the younger man is at the end of the bar, what is the distance of the other man from the end

(a) L/3 (b) L/2 (c) 2L/3 (d) 3L/4 Ans. c (46)

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What is the torque of the force F vector =(2iˆ-3jˆ+4kˆ)Nacting at the pt. r vector = (3iˆ+2jˆ+ 3kˆ)M about the origin

(a) -17iˆ+6jˆ+13kˆ (b) -6iˆ+6jˆ-12kˆ (c) 17iˆ-6jˆ-13kˆ (d) 6iˆ-6jˆ+12kˆ Ans. c (1)

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34. A uniform meter scale balances at the 40 cm mark when weights of 10g and 20g are suspended from the 10 cm and 20cm marks. The weight of the metre scale is

(a) 50g (b) 60g (c) 70g (d) 80g Ans. c (9)

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31. For a system to be in equilibrium, the torques acting on it must balance. This is true only if the torques are taken about

(a) The centre of the system (b) The centre of mass of the system (c) Any point on the system (d) Any point on the system or outside it Ans. d (16)

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30. A couple produces

(a) Purely linear motion (b) Purely rotational motion (c) Linear and rotational motion (d) No motion Ans. b (7)

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26. When a ceiling fan is switched on, it makes 10 rotations in the first 3 seconds. How many rotations will it make in the next 3 seconds (Assume uniform angular acceleration)

(a) 10 (b) 20 (c) 30 (d) 40 Ans. c (11)

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Let F be the force acting on a particle having position vector r vector and T vector be the torque of this force about the origin. Then

(a) r vector X T vector=0 and F vector X T vector =0 (b) r vector X T vector = 0 and F vector x T vector not equal to Zero (c) r vector X T vector not equal to …

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28. Let A vector be a unit vector along the axis of rotation of a purely rotating body and B vector be a unit vector along the velocity of a particle P of the body away from the axis. The value of A vector X B vector is

(a) 1 (b) – 1 (c) 0 (d) None of these Ans. c (7)

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27. When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest (Assume uniform angular retardation)

(a) 36 (b) 24 (c) 18 (d) 12 Ans. d (16)

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25. A rigid body is rotating with variable angular velocity (a-bt) at any instant of time t. The total angle subtended by it before coming to rest will be (a and b are constants)

(a) (a-b)a/2 (b) a2/2b (c) a2-b2/2b (d) a2-b2/2a Ans. b (11)

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24. A sphere is rotating about a diameter

(a) The particles on the surface of the sphere do not have any linear acceleration (b) The particles on the diameter mentioned above do not have any linear acceleration (c) Different particles on the surface have different angular speeds (d) …

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23. The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are 3 rad/sec and 4 rad/sec respectively, then the resultant angular velocity of the system would be

(a) 1 rad/sec (b) 7 rad/sec (c) 5 rad/sec (d) √12 rad/sec Ans. c (610)

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22. A particle starts rotating from rest. Its angular displacement is expressed by the following equationθ =0.025t square-0.1t where θ is in radian and t is in seconds. The angular acceleration of the particle is

(a) 0.5 rad/sec2 at the end of 10 sec (b) 0.3 rad/sec2 at the end of 2 sec (c) 0.05 rad/sec2 at the end of 1 sec (d) Constant 0.05 rad/sec2 Ans. d (31)

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19. Two particles having mass ‘M’ and ‘m’ are moving in circular paths having radii R and r. If their time periods are same then the ratio of their angular velocities will be

(a) r/R (b) R/r (c) 1 (d) √R/r Ans. c (8)

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18. A particle B is moving in a circle of radius a with a uniform speed u. C is the centre of the circle and AB is diameter. The angular velocity of B about A and C are in the ratio

(a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 4 : 1 Ans. b (13)

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17. A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian/s2 is

(a) π/2 (b) π/4 (c) π/6 (d) π/8 Ans. a (5)

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16. A car is moving at a speed of 72 km/hr. the diameter of its wheels is 0.5 m. If the wheels are stopped in 20 rotations by applying brakes, then angular retardation produced by the brakes is

(a) – 25.5 rad/s2 (b) – 29.5 rad/s2 (c) – 33.5 rad/s2 (d) – 45.5 rad/s2 Ans. a (10)

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15. A flywheel gains a speed of 540 r.p.m. in 6 sec. Its angular acceleration will be

(a) 3 pi rad/sec2 (b) 9 pi rad/sec2 (c) 18 pi rad/sec2 (d) 54 pi rad/sec2 Ans. a (43)

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14. The angular speed of a fly–wheel making 120 revolution/minute is

(a) π rad/sec (b) 2π rad/sec (c) 4 π rad/sec (d) 4π2 rad/sec Ans. c (28)

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13. In rotational motion of a rigid body, all particle move with

(a) Same linear and angular velocity (b) Same linear and different angular velocity (c) With different linear velocities and same angular velocities (d) With different linear velocities and different angular velocities Ans.c (7)

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12. Two particles of masses 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the velocity of the centre of mass is

(a) 0.5 m/s (b) 0.75 m/s (c) 1.25 m/s (d) Zero Ans.a (11)

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11. Three identical spheres, each of mass 1 kg are placed touching each other with their centres on a straight line. Their centres are marked K, L and M respectively. The distance of centre of mass of the system from K is

(a) (KL+KM+LM)/3 (b) (KL+KM)/3 (C) (KL+LM)/3 (d) (KM+LM)/3 Ans. b (35)

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