Motion in a Plane · Question 11

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 )