Motion in a Plane

A particle moves in x-y plane according to rule x = a t and y = a t. The particle follows

1. an elliptical path
2. a circular path
3. a parabolic path
4. a straight line path inclined equally to x and y-axes

A particle has initial velocity (3 i + 4 j) and has acceleration (0.4 i + 0.3 j). Its speed after 10 s is

1. 7 units
2. 7 2 units
3. 8.5 units
4. 10 units

Six vectors, a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true? [figure]

1. b + c = f
2. d + c = f
3. d + e = f
4. b + e = f

A particle of mass m is projected with velocity v making an angle of 45 with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :

1. mv 2
2. zero
3. 2mv
4. mv/ 2

A and B are two vectors and θ is the angle between them. If | A B| = 3 ( A B), the value of θ is

1. 45
2. 30
3. 90
4. 60

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are ( 3, 3 ). The path of the particle makes with the x-axis an angle of

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

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is

1. 10 m/s, 0
2. 0, 0
3. 0, 10 m/s
4. 10 m/s, 10 m/s.

For angles of projection of a projectile at angle (45 - ) and (45 + ), the horizontal range described by the projectile are in the ratio of

1. 2 : 1
2. 1 : 1
3. 2 : 3
4. 1 : 2.

The vectors A and B are such that | A + B| = | A - B|. The angle between the two vectors is

1. 45
2. 90
3. 60
4. 75

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is

1. a v2 + v12
2. av + v1
3. av - v1
4. a2v2 - v12

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

1. 2 m s-2 and direction along the radius towards the centre
2. 2 m s-2 and direction along the radius away from the centre
3. 2 m s-2 and direction along the tangent to the circle
4. 2/4 m s-2 and direction along the radius towards the centre.

If the angle between the vectors A and B is , the value of the product ( B A ) A is equal to

1. BA2
2. BA2
3. BA2
4. zero.

If a vector 2 i + 3 j + 8 k is perpendicular to the vector 4 j - 4 i + k, then the value of is

1. 1/2
2. -1/2
3. 1
4. -1.

If | A B| = 3 A B then the value of | A + B| is

1. (A2 + B2 + AB)1/2
2. (A2 + B2 + AB 3 )1/2
3. A + B
4. (A2 + B2 + 3AB)1/2

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

1. are equal to each other
2. are equal to each other in magnitude
3. are not equal to each other in magnitude
4. cannot be predicted.

A particle moves along a circle of radius ( 20 ) m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is

1. 40 m/s2
2. 640 m/s2
3. 160 m/s2
4. 40 m/s2

A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5 m/sec from the same height then correct statement is

1. particle A will reach at ground first with respect to particle B
2. particle B will reach at ground first with respect to particle A
3. both particles will reach at ground simultaneously
4. both particles will reach at ground with same speed.

If | A + B | = | A | + | B |, then angle between A and B will be

1. 90
2. 120
3. 0
4. 60

Two particles having mass M and m are moving in a circular path having radius R and r. If their time periods are the same, then the ratio of their angular velocities will be

1. rR
2. Rr
3. 1
4. Rr

A particle is projected making an angle of 45 with horizontal having kinetic energy K. The kinetic energy at highest point will be

1. K 2
2. K2
3. 2K
4. K

The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river along the shortest path in 15 min. Then the velocity of river stream is

1. 3 km/hr
2. 4 km/hr
3. 29 km/hr
4. 41 km/hr

Two projectiles of same mass and with same velocity are thrown at an angle 60 and 30 with the horizontal, then which will remain same

1. time of flight
2. range of projectile
3. maximum height acquired
4. all of them