Motion in a Plane

For three vectors A = (-x i - 6 j - 2 k), B = (- i + 4 j + 3 k) and C = (-8 i - j + 3 k), if A ( B C) = 0, then value of x is .

The angle between vector Q and the resultant of (2 Q + 2 P) and (2 Q - 2 P) is :

1. -1(P/Q)
2. 0
3. -1 (2 Q - 2 P)2 Q + 2 P
4. -1(2Q/P)

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in m/s2) :

1. 4 2 m s-2
2. 16 2 m s-2
3. 57600 2 m s-2
4. Zero

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is m.

The co-ordinates of a particle moving in x-y plane are given by : x=2+4t, y=3t+8t2. The motion of the particle is :

1. uniform motion along a straight line.
2. non-uniformly accelerated.
3. uniformly accelerated having motion along a straight line.
4. uniformly accelerated having motion along a parabolic path.

Two forces F1 and F2 are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F1 and F2 is -1 ( 1n ). The value of |n| is .

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= .