Motion in a Plane · Question 6

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