Motion in a Plane

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