Motion in a Plane · Question 1

Let 1, 2 and 3 be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If x1, x2 and x3 are their respective angular distances in 1 minute then the factor which remains constant (k) is

1. 1x1 = 2x2 = 3x3 = k
2. 1 x1 = 2 x2 = 3 x3 = k
3. 1 x12 = 2 x22 = 3 x32 = k
4. 12 x1 = 22 x2 = 32 x3 = k

A bullet is fired from a gun at the speed of 280 m s-1 in the direction 30 above the horizontal. The maximum height attained by the bullet is (g = 9.8 m s-2, 30 = 0.5 ) :-

1. 2000 m
2. 1000 m
3. 3000 m
4. 2800 m

A ball is projected with a velocity, 10 m s-1, at an angle of 60 with the vertical direction. Its speed at the highest point of its trajectory will be

1. Zero
2. 5 3 m s-1
3. 5 m s-1
4. 10 m s-1

A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30 above the horizontal. The maximum height attained by the ball during its motion is (g = 10 m/s2)

1. 25 m
2. 5 m
3. 10 m
4. 20 m

If F = 2 i + j - k and r = 3 i + 2 j - 2 k, then the scalar and vector products of F and r have the magnitudes respectively as

1. 10, 2
2. 5, 3
3. 4, 5
4. 10, 2

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, , is then given by :

1. = -1 ( 2gT2 2 R )1/2
2. = -1 ( gT2 2 R )1/2
3. = -1 ( 2 RgT2 )1/2
4. = -1 ( 2 RgT2 )1/2

A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)

1. 20 2 m/s, 10 m/s2
2. 20 m/s, 5 m/s2
3. 20 m/s, 0
4. 20 2 m/s, 0

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :

1. 0
2. 60
3. 45 west
4. 30 west

Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

1. vA : vB
2. 1 : 1
3. rB : rA
4. rA : rB

The x and y coordinates of the particle at any time are x = 5t - 2t2 and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is

1. 5 m s-2
2. -4 m s-2
3. -8 m s-2
4. 0