Motion in a Plane

If a and b make an angle -1 ( 59 ) with each other, then | a + b| = 2| a - b| for | a| = n| b|. The integer value of n is .

The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B. The angle between vectors A and B is .

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take = 3.14) :

1. 118.9
2. 140.5
3. 139.4
4. 220.0

Three vectors OP, OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A x. The value of x is . [figure]

The angle of projection for a projectile to have same horizontal range and maximum height is :

1. -1 ( 12 )
2. -1(2)
3. -1 ( 14 )
4. -1(4)

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2 M thrown at a velocity v2 from the top of the tower of height 4H will touch the ground at a distance of m.

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.