Tiêu đề 4.MOTION IN A PLANE - Questions.pdf ✅

4.MOTION IN A PLANE (1.)A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is (a.) Zero (b.) 30° (c.) 45° (d.) 60° (2.)What is the smallest radius of a circle at which a cyclist can travel if its speed is 36 kmh −1 , angle of inclination 45° and g = 10ms −2 ? (a.) 20 m (b.) 10 m (c.) 30 m (d.) 40 m (3.)In uniform circular motion (a.) Both the angular velocity and the angular momentum vary (b.) The angular velocity varies but the angular momentum remains constant (c.) Both the angular velocity and the angular momentum stay constant (d.) The angular momentum varies but the angular velocity remains constant (4.)A small disc is on the top of a hemisphere of radius R. What is the smallest horizontal velocity v that should be given to the disc for it to leave the hemisphere and not slide down it? [There is no friction] (a.) v = √2gR (b.) v = √gR (c.) v = g R (d.) v = √g2R (5.)An aeroplane is flying with a uniform speed of 100 m/s along a circular path of radius 100 m. the angular speed of the aeroplane will be (a.) 1 rad/sec (b.) 2 rad/sec (c.) 3 rad/sec (d.) 4 rad/sec (6.)If A⃗ 1 and A⃗ 2 are two non-collinear unit vectors and if |A⃗ 1 + A⃗ 2 | = √3, then the value of (A⃗ 1 − A⃗ 2)∙ (2A⃗ 1 + A⃗ 2) is (a.) 1 (b.) 1/2 (c.) 3/2 (d.) 2 (7.)Given A⃗ = 4î+ 6ĵand B⃗ = 2î+ 3ĵ. Which of the following is correct? (a.) A⃗ × B⃗ = 0⃗ (b.) A⃗ ∙ B⃗ = 24 (c.) |A⃗ | |B⃗ | = 1 2 (d.) A⃗ and B⃗ are anti-parallel (8.)A body of mass m kg is rotating in a vertical circle at the end of a string of length r metre. The difference in the kinetic energy at the top and bottom of the circle is (a.) mg r (b.) 2mg r (c.) 2mgr (d.) mgr (9.)Radius of the curved road on national highway is R. Width of the road is b. The outer edge of the road is raised by h with respect to inner edge so that a car with velocity v can pass safe over it. The value of h is (a.) v 2b Rg (b.) v Rgb (c.) v 2R g (d.) v 2b R (10.)Consider a vector F⃗ = 4î− 3ĵ. Another vector that is perpendicular to F⃗ is (a.) 4î+ 3ĵ (b.) 6ĵ (c.) 7ĵ (d.) 3î− 4ĵ (11.)A particle moves in a circular path with decreasing speed. Choose the correct statement (a.) Angular momentum remains constant (b.) Acceleration (a ) is towards the centre (c.) Particle moves in a spiral path with decreasing radius (d.) The direction of angular momentum remains constant (12.)A proton in a cyclotron changes its velocity from 30kms −1 north to 40kms −1 east in 20 s. what is the average acceleration during this time (a.) 2.5 kms −2 at 37° E of S (b.) 2.5 kms −2 at 37° N of E (c.) 2.5 kms −2 at 37° N of S (d.) 2.5 kms −2 at 37° E of N
(13.)Which one of the following statements is not correct in uniform circular motion (a.) The speed of the particle remains constant (b.) The acceleration always points towards the centre (c.) The angular speed remains constant (d.) The velocity remains constant (14.)A boy playing on the roof of a 10 m high building throws a ball with a speed of 10ms −1 at an angle of 30° with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? [g = 10ms −2 , sin 30° = 1/ 2, cos 60° = √3/2] (a.) 5.20 m (b.) 4.33 m (c.) 2.60 m (d.) 8.66 m (15.)A particle of mass m is circulating on a circle of radius r having angular momentum L, then the centripetal force will be (a.) L 2 /mr (b.) L 2m/r (c.) L 2 /mr 3 (d.) L 2 /mr 2 (16.)The maximum height attained by a projectile when thrown at an angle θ with the horizontal is found to be half the horizontal range. Then θ is equal to (a.) tan−2 (2) (b.) π 6 (c.) π 4 (d.) tan−1 ( 1 2 ) (17.)A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms −2 , then the maximum angular velocity of the stone will be (a.) 4 radians/sec (b.) 16 radians/sec (c.) √21 radians/sec (d.) 2 radians/sec (18.)A particle is moving with velocity v = K(yî+ xĵ), where K is a constant. The general equation for its path is (a.) y 2 = x 2 + constant (b.) y = x 2 + constant (c.) y 2 = x + constant (d.) xy = constant (19.)A projectile fired with initial velocity u at some angle θ has a range R. If the initial velocity be doubled at the same angle off projection, then the range will be (a.) 2R (b.) R/2 (c.) R (d.) 4R (20.)A particle is moving with velocity v = k(yi̇ ̂ + x j̇ ̂), where k is a constant. The general equation for its path is (a.) y = x 2 + constant (b.) y 2 = x + constant (c.) xy = constant (d.) y 2 = x 2 constant (21.)A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly (a.) 14 rpm (b.) 10 rpm (c.) 2.25 rpm (d.) 7 rpm (22.)If a stone s to hit at a point which is at a distance d away and at a height h above the point from where the stone starts, then what is the value of initial sped u, if the stone is launched at an angle Q? (a.) g cosθ √ d 2(d tan θ−h) (b.) d cosθ √ g 2(d tan θ−h) (c.) √ gd2 h cos2 θ (d.) √ gd2 (d−h) (23.)The horizontal range of an oblique projectile is equal to the distance through which a projectile has to fall freely from rest to acquire a velocity equal to the velocity of projection in magnitude. The angle of projection is (a.) 75° (b.) 60° (c.) 45° (d. ) 30° (24.)A ball is projected up an incline of 30° with a velocity of 30 ms −1 at an angle of 30° with reference to the inclined plane from the bottom of the inclined plane. If g = 10ms −2 , then the range on the inclined plane is (a.) 12 m (b.) 60 m
(c.) 120 m (d.) 600 m (25.)For a particle in uniform circular motion the acceleration a at a point P(R, θ) on the circle of the radius R is (here θ is measured from the x −axis) (a.) − v 2 R cos θ i̇ ̂ + v 2 R sin θ j̇ ̂ (b.) − v 2 R sin θ i̇ ̂ + v 2 R cos θ j̇ ̂ (c.) − v 2 R cos θ i̇ ̂ − v 2 R sinθ j̇ ̂ (d.) − v 2 R i̇ ̂ + v 2 R j̇ ̂ (26.)If the resultant of A⃗ and B⃗ makes angle α with A⃗ and β with B⃗ then (a.) α < β always (b.) α < β, if A < B (c.) α < β, if A > B (d.) α < β, if A = B (27.)A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change (a.) 1 ∶ 4 (b.) 1 4 : 2 (c.) 2 ∶ 1 (d.) 4 ∶ 1 (28.)A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following (a.) Straight path (b.) Circular path (c.) Parabolic path (d.) Hyperbolic path (29.)The velocity of projection of an oblique projectile is v⃗ = 3î+ 2ĵ(in ms −1 ). The speed of the projectile at the highest point of the trajectory is (a.) 3 ms −1 (b.) 2 ms −1 (c.) 1 ms −1 (d.) Zero (30.)A roller coaster is designed such that riders experience ‘weightlessness’ as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top the hill is between (a.) 14 ms−1 and 15 ms−1 (b.) 15 ms−1 and 16 ms−1 (c.) 16 ms−1 and 17 ms−1 (d.) 13 ms−1 and 14 ms−1 (31.)A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v. If the string is released, the stone flies (a.) Radially outwards (b.) Radially inwards (c.) Tangentially outwards (d.) With an acceleration mv 2 /l (32.)A projectile is projected with velocity kve in vertically upward direction from the ground into the space (ve is the escape velocity andk < 1). If air resistance is considered to be negligible then the maximum height from the center of earth to which it can go will be (R = radus of earth) (a.) R k 2+1 (b.) R k 2−1 (c.) R 1−k 2 (d.) R k+1 (33.)A car is moving along a straight horizontal road with a speedv0. If the coefficient of friction between tyres and the road is μ, the shortest distance in which the car can be stopped is (a.) v0 2 2μg (b.) v0 μg (c.) ( v0 μg) 2 (d.) v0 μ (34.)A particle is projected with a velocity 200 ms −1 at an angle of 60°. At the highest point, it explodes into three particles of equal masses. One goes vertically upwards with a velocity 100 ms −1 , the second particle goes vertically downwards. What is the velocity of third particle? (a.) 120 ms −1 making 60° angle with horizontal (b.) 200 ms −1 making 60° angle with horizontal (c.) 300 ms −1 (d. ) 200 ms −1 (35.)A car is moving with speed 30 m/sec on a circular path of radius 500 m. Its speed is increasing at the rate of 2m/ sec2 , What is the acceleration of the car (a.) 2m/ sec2 (b.) 2.7m/ sec2 (c.) 1.8m/ sec2 (d.) 9.8m/ sec2 (36.)Given, P⃗ = A⃗ +B⃗ and P = A + B. The angle between A⃗ and B⃗ is (a.) 0° (b.) π 4 (c.) π 2 (d.) π (37.)The angular amplitude of a simple pendulum is θ0. The maximum tension in its string will be (a.) mg(1 − θ0) (b.) mg(1 + θ0) (c.) mg(1 − θ0 2 ) (d.) mg(1 + θ0 2 )
(38.)The angle turned by a body undergoing circular motion depends on time as θ = θ0 + θ1t + θ2t 2 . Then the angular acceleration of the body is (a.) θ1 (b.) θ2 (c.) 2θ1 (d.) 2θ2 (39.)Toy cart tied to the end of an unstretched string of length a, when revolved moves in a horizontal circle of radius 2a with a time period T. Now the toy cart is speeded up until it moves in a horizontal circle of radius 3a with a period T′. If Hook’s law holds then (a.) T ′ = √ 3 2 T (b.) T ′ = ( √3 2 ) T (c.) T ′ = ( 3 2 ) T (d.) T ′ = T (40.)A ball is projected with kinetic energy E at an angle of 45° to the horizontal. At the highest point during its flight, its kinetic energy will be (a.) Zero (b.) E 2 ⁄ (c.) E √2 ⁄ (d.) E (41.)A particle of mass m moves with constant speed along a circular path of radius r under the action of force F. Its speed is (a.) √Fr/m (b.) √F/r (c.) √F m r (d.) √F/mr (42.)If a body is projected with an angle θ to the horizontal then (a.) its velocity is always perpendicular to its acceleration (b.) its velocity becomes zero as its maximum height (c.) its velocity makes zero angle with the horizontal at its maximum height (d.) the body just before hitting the ground, the direction of velocity coincides with the acceleration (43.)Tom and Dick are running forward with the same speed. They are throwing a rubber ball to each other at a constant speed v as seen by the thrower. According to Sam who is standing on the ground the speed of the ball is (a.) Same as v (b.) Greater than v (c.) Less than v (d.) None of these (44.)The adjacent sides of a parallelogram are represented by co-initial vectors 2î+ 3ĵand î+ 4ĵ. The area of the parallelogram is (a.) 5 units along z-axis (b.) 5 units in x − y plane (c.) 3 units in x − z plane (d.) 3 units in y − z plane (45.)An aeroplane is flying horizontally with a velocity of 216 kmh −1 and at a height of 1960 m. When it is vertically above a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is (ignoring air resistance) (a.) 1200 m (b.) 0.33 km (c.) 3.33 km (d.) 33 km (46.)A projectile is thrown with a speed u at an angle θ to the horizontal. The radius of curvature of its trajectory when the velocity vector of the projectile makes an angle α with the horizontal is (a.) u 2 cos2 α gcos 2 θ (b.) 2u 2 cos2 α gcos 2 θ (c.) u 2 cos2 θ gcos 3 α (d.) u 2 cos2 θ gcos 2 α (47.)A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle θ1. In the next 2 sec, it rotates through an additional angle θ2. The ratio of θ2 /θ1 is (a.) 1 (b.) 2 (c.) 3 (d.) 5 (48.)In uniform circular motion, the velocity vector and acceleration vector are (a.) Perpendicular to each other (b.) Same direction (c.) Opposite direction (d.) Not related to each other (49.)A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 m/s. At what angle from horizontal the ball must be fired so that it hits the pirate ship (a.) 54° (b.) 125° (c.) 27° (d.) 18° (50.)A particle is projected from horizontal making an angle 60° with initial velocity 40ms −1 . The time