Motion in a Plane

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle to the horizontal, the maximum height attained by it is equal to 4R. The angle of projection is then given by :

1. -1 [ 2gT2 2R ] 12
2. -1 [ 2R2gT2 ] 12
3. -1 [ 2gT2 ] 12
4. -1 [ 2gT2 2R ] 12

If two vectors A and B having equal magnitude R are inclined at angle , then

1. | A+ B|=2R ( 2 )
2. | A- B|=2R ( 2 )
3. | A- B|= 2R ( 2 )
4. | A+ B|=2R ( 2 )

Projectiles A and B are thrown at angles of 45 and 60 with vertical respectively from top of a 400 m high tower. If their ranges and times of flight are same, the ratio of their speeds of projection vA:vB is : [Take g=10 m s-2]

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

A vector has magnitude same as that of A=3 i+4 j and is parallel to B=4 i+3 j. The x and y components of this vector in first quadrant are x and 3 respectively where x= .

A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 m high and 0.1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be x ms-1 where x= [use g=10 m/s2].

A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t=0 is 4 m/s, the time taken to complete the first revolution will be 1 [1-e-2 ]s, where = .

Position of an ant (S in metres) moving in Y-Z plane is given by S=2t2 j+5 k (where t is in second). The magnitude and direction of velocity of the ant at t=1 s will be :

1. 16 m/s in y-direction
2. 4 m/s in x-direction
3. 9 m/s in z-direction
4. 4 m/s in y-direction

A particle starts from origin at t = 0 with a velocity 5 i m/s and moves in x-y plane under action of a force which produces a constant acceleration of (3 i + 2 j) m/s2. If the x-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is m/s. The value of is .