Motion in a Plane

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