A car A is going north-east at 80 km/h and another car B is going south-east at 60 km/h. The velocity of A relative to B makes an angle with the north equal to: (a) (b) (c) (d) The velocity of a boat in still water is n times less than the velocity of flow of water (n > 1). The angle with the stream direction at which the boat must move to minimize drifting: (a) (b) 90 + (c) (d) 90 + Two cars start simultaneously along two straight lines at an angle from the same point. One moves with uniform velocity u and the other with a uniform acceleration a. The least value of relative velocity will be at time given by: (a) (b) (c) (d) In problem 3, the least value of the relative velocity is: (a) u cos (b) u sin (c) u cot (d) u sec Of the sets given below, the one that may represent the magnitudes of three vectors adding to zero: (a) 1, 2, 4 (b) 2, 3, 6 (c) 4, 5, 9 (d) 1, 1, 3 Find the incorrect answer.The y-component of the resultant of several vectors:(a) may be greater than the sum of the magnitudes of the vectors(b) may be smaller than the sum of the magnitudes of the vectors(c) may be equal to the sum of the magnitudes of the vectors(d) is equal to the sum of the y- components of the vectorsAn aircraft is flying due West in a cross-wind that blows from north to south. The pilot draws the following vector diagram to establish the aircraft's correct heading. What is the correct label for the vector marked Z in the diagram? (a) Resultant velocity of aircraft relative to the ground (b) Velocity of aircraft relative to the ground (c) Velocity of air relative to the ground (d) Velocity of aircraft relative to the airFour forces acting on a particle keep it at rest. Then the correct statements are: (i) The forces must be coplanar (ii) The forces cannot be coplanar (iii) The forces may or may not be coplanar (iv) If three of the forces are coplanar, so must be the fourth (a) i, ii, iii (b) i, iii, iv (c) i, iv (d) iii, ivThree horizontal forces of equal magnitude act on a box at rest as shown in the diagram. The box: (a) accelerates towards the north-east (b) accelerates towards the south-east (c) accelerates towards the south-west (d) does not accelerateA body is just being revolved in a vertical circle of radius 20 m. The string breaks when the body is at the highest point. The horizontal distance covered by the body after the string break is given by: (a) 10 m (b) 20 m (c) 40 m (d) zeroA particle is placed at the highest point of a frictionless hemispherical surface. If the particle is allowed to slide down, the angular displacement at which it will leave the surface is: (a) cos (b) cos (c) cos (d) cos A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed center at an angular velocity . If the length of the string and angular velocity are doubled, the tension in the string which was initially T is now: (a) T (b) T/2 (c) 4 T (d) 8 TThe speed of revolution of a particle is going around a circle is doubled and its angular speed is halved. What happens to the centripetal acceleration?: (a) Remains unchanged (b) Halved (c) Doubled (d) Becomes four timesWhen the angular velocity of a uniformly rotating body is increased thrice, the resultant force applied to it increases by 60 N. If the mass of the body = 3 kg, the initial and final accelerations are: (a) 2.5m/s, 7.5m/s (b) 7.5m/s, 22.5m/s (c) 5m/s, 45m/s (d) 2.5m/s, 22.5m/sTwo particles of masses m and m are moving in concentric horizontal circles of radii r and r respectively, such that their periods are same. The ratio of their centripetal accelerations is: (a) r1 /r2 (b) r2/r1 (c) (r1/r2)2 (d) m1 r1 /m2r2A coin placed on a rotating turn table just slips if it is at a distance of 4 cm from the centre. If the angular velocity of the turn table is doubled, it will just slip at a distance of: (a) 1 cm (b) 2 cm (c) 4 cm (d) 8 cmThe speed of a particle is increasing at a constant rate a. Which of the following graphs shows the variation of centripetal force F with time t: (a) (b) (c) (d) A particle performing uniform circular motion has: (a) radial velocity and radial acceleration (b) radial velocity and transverse acceleration (c) tangential velocity and radial acceleration (d) tangential velocity and tangential accelerationThe resultant of two forces 3 P and 2P is R. If the first force is doubled, the resultant is also doubled. The angle between the two forces is: (a) 600 (b) 900 (c) 1200 (d) 1800 A body has an initial velocity of 30 m/s along a horizontal direction. If the body is moving with a constant acceleration of 5 m/s2 whose direction is at 90° with the horizontal, then its velocity after 5 sec will be: (a) 55 m/s (b) 50 m/s (c) 39 m/s(d) 20 m/sThree vectors, and are such that = + and their magnitudes are 10, 8 and 6 respectively. The angle between and is: (a) sin-1 (3/5) (b) sin-1 (4/5) (c) cos-1(3/5) (d) cos-1(4/5)A particle moves from position 5 + 2 4 to position 16 + 12 + 8 in metres when a uniform force 6 + 4 + 2 N acts on it. The work done by the force is: (a) 100 Joule (b) 180 Joule (c) 50 Joule (d) 126 JouleAn object of mass 3 kg is at rest. Now a force of = 6t2 + 4t is applied on the object then velocity of object at t = 3 sec is: (a)18+3(b) 18+6 (c) 18+4 (d) 3+18A boat is moving with a velocity = 3 + 4 with respect to the ground, the water in the river is flowing with a velocity = 3 4 with respect to ground. Then the relative velocity of the boat with respect to water is: (a) 6 + 4 (b) 6 8 (c) 3 8 (d) 6 + 8Rain is falling vertically downwards with a velocity 4 km/hour. A cyclist moves on a C straight road with a velocity 3 km/hour. Then the apparent velocity of the rain with respect to the cyclist is: (a) 7km/hour (b) 1 km/hour (c) 5 km/hour(d) 4 km/hourIf the sum of two unit vectors is a unit vector, then the magnitude of their difference is: (a) (b) 3 (c) 2 (d) A car is going towards north wit a speed of 20 m/s. It turns to west and continues with the same speed. The change in its velocity will be: (a) 40 m/s north-west (b) 20 m/s north-east (c) 40 m/s south-west (d) 20 m/s south-west The trajectory of a projectile in a vertical plane is y = ax - bx2, where a and b are constants, and x and y are the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the projectile is: (a) (b) (c) (d) A gun kept on a straight horizontal road, is used to hit a car travelling along the same road away from the gun with a uniform speed of 72 km/hr. The car is at a distance of 500 m from the gun when the gun is fired at an angle of 45° with the horizontal. The distance of the car from the gun when the shell hits it, is: (a) 74.7 m(b) 747 m (c) 148 m (d) 352 mThe maximum range of a projectile projected with some initial velocity i5 found to be 1000 m. The maximum height reached by this projectile is: (a) 250 m (b) 500 m (c) 700 m (d) 2000 mA bullet is fired with a velocity u at an angle θ horizontal, then its speed when the direction of motion makes an angle α with the horizontal: (a) u cos θ (b) u cos θ cos α (c) u cos θ sin α (d) Two particles are separated by a horizontal distance X as shown in the adjoining figure. They are projected at the same time with velocities and u respectively. The time after which the horizontal distance between the particles becomes zero, is: (a) (b) (c) (d) A plane flying horizontally at a height of 1500 m with a velocity of 200 m/s passes directly over an aircraft gun. Then the angle with the horizontal at which the gun be fired for the shell with a muzzle velocity of 400 m/sec to hit the plane, is: (a) 90°(b) 60° (c) 30°(d) 45°In the above question the minimum height at which the plane should fly to avoid being hit by the shell is: (a) 1500 m (b) 3000 m (c) 6000 m (d) 12,000 mA stone is projected from the ground with a velocity of 50 m/s at an angle of 300. It crosses a wall after 4 s. The distance beyond the wall at which the stone strikes the ground is: (a) 25 m(b) 30 m (c) 35 m (d) 25 mA particle of mass m is executing uniform circular motion on a path of radius r. If P is the magnitude of linear momentum, the radial- force acting on the particle is: (a) (b) (c) (d) A car takes a circular turn with a uniform speed v. If the reaction at the inner and outer wheels be denoted by Rl and R2, then: (a) Rl = R2 (b) Rl < R2 (c) Rl < R2(d) Rl < 2R2A 1000 kg car is moving with a uniform speed of 30 m/s on a circular path of radius 200 m. The frictional force required to provide the necessary centripetal force to the car is: (a) 2250N(b) 9000N (c) 4500N(d) 1000NAn aero plane loops the loop of radius 500 m in a vertical plane with a uniform speed of 100 m/s. If the mass of the pilot be 80 kg, then the apparent weight of the pilot at the lowest, middle and uppermost points of the loop is: (a) 2400 N, 1600 N, 800 N (b) 800 N , 1600 N, 2400 N (c) 2400 N, 800 N ,1600 N (d) 800 N ,2400 N, 1600 NIf water and mercury are rotated in a cylindrical tube, then: (a) water will be forced to the outer part (b) mercury will be forced to outer part (c) water and mercury will be mixed up (d) it depends upon the speed of rotationA string can bear a maximum tension of 100 N without breaking. A mass of 1 kg is tied to one end of a 1 m long piece of the string and rotated in a horizontal plane. The maximum linear velocity with which it can be rotated is: (a) 5 m/s (b) 10 m/s (c) 15 m/sec(d) 10 cm/sA tube of length L is filled completely filled with an incompressible liquid of mass m and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity. The force exerted by the liquid at the other end is: (a) (b) (c) (d) A particle crosses the top most point A of a vertical circle with a critical speed, then the ratio of velocities at the point A, B and C is: (a) 1:2:3 (b) 1:3:5 (c) 12:32:52 (d) ::A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m. The angle made by the rod with the track is: (a) zero(b) 39° (c) 45° (d) 60°The length of second's needle in a watch is 1.2 cm. The velocity of the tip of the needle in cm/ sec is: (a) 2π × 1.2 (b) (c) (d) A cyclist moves around a circular path of radius 39.2 m with a speed of 19.6 m/s. Then the angle at which he should bend himself is given by: (a) 45°(b) 30°(c) 60°(d) tan-l (2)On switching off a fan, its angular velocity reduces to half of its initial one in making 12 revolutions. After how many additional revolutions it will come to rest? (a) 4(b) 3 (c) 6(d) 12A simple pendulum with a bob of point mass m and length r is made to move along a circular path in the vertical plane. v is the velocity of the bob at the lowest point in the path, then the bob oscillates when: (a) v > (b) v = (c) v < (d) < v < The greatest height to which a man can throw a stone is h. The greatest range to which he throw will be: (a) h(b) 2h (c) 3h(d) h/2 The range of a projectile when launched at an angle of 150 with the horizontal is 1.5 km. If it is launched at an angle of 450 with the horizontal, its range will be: (a) 1.5 km (b) 3.0 km (c) 6.0 km (d) 7.5 km