Motion in a Plane

A particle moving with uniform speed in a circular path maintains:

1. Constant velocity
2. Constant acceleration
3. Constant velocity but varying acceleration
4. Varying velocity and varying acceleration

Let 1, 2 and 3 be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If x1, x2 and x3 are their respective angular distances in 1 minute then the factor which remains constant (k) is

1. 1x1 = 2x2 = 3x3 = k
2. 1 x1 = 2 x2 = 3 x3 = k
3. 1 x12 = 2 x22 = 3 x32 = k
4. 12 x1 = 22 x2 = 32 x3 = k

A bullet is fired from a gun at the speed of 280 m s-1 in the direction 30 above the horizontal. The maximum height attained by the bullet is (g = 9.8 m s-2, 30 = 0.5 ) :-

1. 2000 m
2. 1000 m
3. 3000 m
4. 2800 m

A ball is projected with a velocity, 10 m s-1, at an angle of 60 with the vertical direction. Its speed at the highest point of its trajectory will be

1. Zero
2. 5 3 m s-1
3. 5 m s-1
4. 10 m s-1

A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30 above the horizontal. The maximum height attained by the ball during its motion is (g = 10 m/s2)

1. 25 m
2. 5 m
3. 10 m
4. 20 m

If F = 2 i + j - k and r = 3 i + 2 j - 2 k, then the scalar and vector products of F and r have the magnitudes respectively as

1. 10, 2
2. 5, 3
3. 4, 5
4. 10, 2

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, , is then given by :

1. = -1 ( 2gT2 2 R )1/2
2. = -1 ( gT2 2 R )1/2
3. = -1 ( 2 RgT2 )1/2
4. = -1 ( 2 RgT2 )1/2

A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)

1. 20 2 m/s, 10 m/s2
2. 20 m/s, 5 m/s2
3. 20 m/s, 0
4. 20 2 m/s, 0

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :

1. 0
2. 60
3. 45 west
4. 30 west

Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

1. vA : vB
2. 1 : 1
3. rB : rA
4. rA : rB

The x and y coordinates of the particle at any time are x = 5t - 2t2 and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is

1. 5 m s-2
2. -4 m s-2
3. -8 m s-2
4. 0

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

1. 45
2. 180
3. 0
4. 90

A particle moves so that its position vector is given by r = t x + t y, where is a constant. Which of the following is true?

1. Velocity is perpendicular to r and acceleration is directed towards the origin.
2. Velocity is perpendicular to r and acceleration is directed away from the origin.
3. Velocity and acceleration both are perpendicular to r
4. Velocity and acceleration both are parallel to r

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 10-4 J by the end of the second revolution after the beginning of the motion?

1. 0.18 m/s2
2. 0.2 m/s2
3. 0.1 m/s2
4. 0.15 m/s2

In the given figure, a = 15 m s-2 represents the total acceleration of particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is [figure]

1. 4.5 m s-1
2. 5.0 m s-1
3. 5.7 m s-1
4. 6.2 m s-1

If vectors A = t i + t j and B = t2 i + t2 j are functions of time, then the value of t at which they are orthogonal to each other is

1. t =
2. t = 0
3. t = 4
4. t = 2

The position vector of a particle R as a function of time is given by R = 4 (2 t) i + 4 (2 t) j. Where R is in meters, t is in seconds and i and j denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

1. Magnitude of the velocity of particle is 8 meter/second.
2. Path of the particle is a circle of radius 4 meter.
3. Acceleration vector is along - R.
4. Magnitude of acceleration vector is v2R where v is the velocity of particle.

Two particles A and B, move with constant velocities v1 and v2. At the initial moment their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is

1. r1 v1 = r2 v2
2. r1 - r2 = v1 - v2
3. r1 - r2| r1 - r2| = v2 - v1| v2 - v1|
4. r1 v1 = r2 v2

A ship A is moving Westwards with a speed of 10 km h-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-1. The time after which the distance between them becomes shortest, is

1. 5 2 h
2. 10 2 h
3. 0 h
4. 5 h

A projectile is fired from the surface of the earth with a velocity of 5 m s-1 and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m s-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m s-2) is (Given g = 9.8 m s-2)

1. 3.5
2. 5.9
3. 16.3
4. 110.8

A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector ( vav) from t = 0 to t = 5 s is

1. 15 (13 i + 14 j )
2. 73 ( i + j )
3. 2 ( i + j )
4. 115 ( i + j )

The velocity of a projectile at the initial point A is (2 i + 3 j) m/s. Its velocity (in m/s) at point B is [figure]

1. 2 i - 3 j
2. 2 i + 3 j
3. -2 i - 3 j
4. -2 i + 3 j

Vectors A, B and C are such that A B = 0 and A C = 0. Then the vector parallel to A is

1. A B
2. B + C
3. B C
4. B and C

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

1. = -1 ( 14 )
2. = -1(4)
3. = -1(2)
4. = 45

A particle has initial velocity (2 i + 3 j ) and acceleration (0.3 i + 0.2 j ). The magnitude of velocity after 10 seconds will be

1. 9 2 units
2. 5 2 units
3. 5 units
4. 9 units

A projectile is fired at an angle of 45 with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

1. 45
2. 60
3. -1 ( 12 )
4. -1 ( 32 )

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 s. The acceleration of the particle is

1. 15 m/s2
2. 25 m/s2
3. 36 m/s2
4. 5 m/s2

A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is

1. 40 m
2. 50 m
3. 60 m
4. 20 m

A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is

1. 1 m/s2
2. 7 m/s2
3. 7 m/s2
4. 5 m/s2

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

1. 60
2. 15
3. 30
4. 45