WorksheetsMotion in Two and Three Dimension
Total questions: 48
Worksheet time: 24mins
The x and y coordinates of the particle at any time are x = 5t 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
0
5 m/s2
-4 m/s2
-8m/s2
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
90°
45°
180°
0°
In the given figure, α = 15 m/s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 25 m at a given instant of time. The speed of the particle is
4.5 m/s
5.0 m/s
5.7 m/s
6.2 m/s
A ship A is moving Westwards with a speed of 10 km h-1 and ship B 100 km South of A, is moving Northwards with a speed of 10 km h-1, The time after which the distance between them becomes shortest is
0 h
5
5√2h
10√2h
Two particles A and B, move with constant velocities v1 and v2, At the initial moment their position vectors are r1 and r2 respectively. The condition for particle and B for their collision is
r1 -r2 / ∣ r1 -r2 ∣ = v2-v1 / ∣ v2 -v1 ∣
r1 .v1 = r2 .v2
r1 × v1 = r2 × v2
r1 - r2 = v1-.v2
Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r / 2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of value of heavier stone when they experience same centripetal forces. The value of n is
2
3
4
1
The position vector of a particle R as a function of time is given by
R = 4 sin (2πt) Î +4cos (2πt) ĵ
where R is in metre,t is in second and Î and ĵ denote unit vectors along x and y directions respectively. Which one of the following statements is wrong the motion of particle ?
Acceleration is along -R
Magnitude of acceleration vector is v2/R where v is the velocity of particle
Magnitude of the velocity of particle is 8 m/s
Path of the particle is a circle of radius 4 m
A projectile is fired from the surface of the earth with a velocity of 5 ms-1 at angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in ms-2) is (given, g = 9.8 ms -2)
3.5
5.9
16.3
110.8
A particle is moving such that its position co -ordinates (x,y) are (2m, 3m) at time t = 0, (6m,7m) at time t = 2 s and (13m,14m) at time t = 5 s.
Average velocity vector (ν αν) from t = 0 to t = 5 s is
i/5 (15Î + 14ĵ)
7/3 (î +ĵ)
2(î +ĵ)
11/5(î +ĵ)
The velocity of a projectile at the initial point A is (2î +3ĵ) m/s. Its velocity (in m/s) at point B is
-2Î -3ĵ
-2Î + 3ĵ
2Î -3ĵ
2Î +3ĵ
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is
θ =tan -1 (1/4)
θ =tan -1 (4)
θ =tan -1 (2)
θ =45°
A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2 the range of the missile is
50 m
60 m
20 m
40 m
A particle has initial velocity (3Î + 4ĵ). Its speed after 10 s is
7 unit
7√2 unit
8.5 unit
10 unit
Six vectors a to f have the magnitude and directions indicated in the figure.Which of the following statements is true ?
b+c =f
d +c =f
d +e =f
b+e =f
A particle of mass m is projected with velocity ν making an angle of 45° with the horizontal.When the particle lands on the level ground, the magnitude of the change in its momentum will be
2mv
mv /√2
mv√2
zero
A and B are two vectors and θ is the angle between them. if ∣ A × B∣ = √3(A.B), then the value of θ is
60°
45°
30°
90°
A particle starting from the origin (0,0) moves in a straight line in the (x,y) plane. Its co-ordinates at a later time are (√3,3. The path of the particle makes with the x -axis an angle of
30°
45°
60°
0°
A car runs at a constant speed on a circular track of radius 100 m taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap respectively is
0.0
0.10m/s
10 m/s.10m/s
10 m/s.0
For angles of projection of a projectile at angles (45° +θ), the horizontal ranges described by the projectile are in the ratio of
1:1
2:3
1:2
2:1
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 s, what is the magnitude and direction of acceleration of the stone?
π2 /4 ms-2 and direction along the radius towards the centre
π2 ms-2 and direction along the radius away from the centre
π2 ms-2 and direction along the radius towards the centre
π2 ms-2 and direction along the tangent to the centre
If a vector 2Î +3ĵ +8ķ is perpendicular to the vector 4ĵ -4î +αķ, then the value of α is
-1
1/2
-1/2
1
The circular motion of a particle with constant speed is
simple harmonic but not periodic
periodic and simple harmonic
neither periodic nor simple harmonic
periodic but not simple harmonic
If ∣A ×B∣ =√3A.B, then the value of ∣A + B∣ is
(A2 +B2 + AB)1/2
(A2 +B2 + AB/ √3)1/2
A+B
(A2 +B2 + √3 AB)1/2
The vector sum of two forces is perpendicular to their vector difference.In that case, the forces
are not equal to each other in magnitude
cannot be predicted
are equal to each other
are equal to each other in magnitude
A particle moves along a circle of radius
(20/π) m with constant tangential
acceleration. If the velocity of the particle 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is
160 π m/s2
40 m/s2
40 π m/s2
640 π m/s2
P is the point of contact of a wheel and the ground. The radius of wheel is 1m. The wheel rolls on the ground without slipping.The displacement of point P when wheel completes half rotation is
2 m
√π2 +4 m
π m
√π2 +42m
A stone is attached to one end of a string and rotated in a vertical circle. If string breaks at the position of maximum tension it will break at
A
B
C
D
Two particles are projected with same initial velocities at an angle 30° and 60° with the horizontal. Then
their heights will be equal
their ranges will be equal
their time of flights will be equal
their ranges will be equal different
What is the linear velocity, if angular velocity vector ω = 3Î - 4ĵ +ķ and position vector r = 5Î - 6ĵ +6ķ ?
6Î + 4ĵ - 3ķ
-18Î - 13ĵ +2ķ
18Î + 13ĵ -2ķ
6Î - 2ĵ +8ķ
A person swims in a river aiming to reach exactly opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle 120° with the direction of flow of water. The speed of water in stream is
1.0 m/s
0.5 m/s
0.25 m/s
0.43 m/s
If a unit vector is represented by 0.5Î +0.8ĵ + cķ , then the value of c is
1
√0.11
√0.01
0.39
Two particles A and B are connected by a rigid rod AB.The rod slides along perpendicular rails as shown here. The velocity of A to the right is 10 m/s. What is the velocity of B when angle α = 60° ?
9.8 m/s
10 m/s
5.8 m/s
17.3 m/s
The speed of a boat is 5 km/h in still water. It crosses a river of width 1.0 km along the shortest possible path in 15 min. The velocity of the river water us (in km/h)
5
1
3
4
Find the torque of α force F = -3Î+ĵ +5ķ acting at the point r = 7Î+3ĵ +ķ.
-21Î+3ĵ +5ķ
-14Î+3ĵ -16ķ
4Î+4ĵ +6ķ
14Î-38ĵ +16ķ
A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at any point on circular path ?
√2 m/s
2 m/s
10 m/s
20 m/s
A bullet is fired from a gun with a speed of 1000m/s in order to hit a target 100 m away. At what height above the target should the gun be aimed ? ( The resistance of air is negligible and g = 10 m/s2)
5 cm
10 cm
15 cm
20 cm
The position vector of a particle is r =(αcosωt) Î +(α sin ωt) ĵ. The velocity of particle is
directed towards the origin
directed away from the origin
parallel to the position vector
perpendicular to the position vector
Which of the following is not a vector quantity ?
Speed
Velocity
Torque
Displacement
The angle between the two vectors
A =3Î +4ĵ +5ķ and B =3Î +4ĵ - 5ķ will be
0°
45°
90°
180°
A boat is sent across a river with a velocity of 8 km h-1. If the resultant velocity of boat is 10 km h-1, then velocity of river is
12.8 km h-1
6 km h-1
8 km h-1
10 km h-1
The resultant of A × 0 will be equal to
zero
A
zero vector
unit vector
When milk is churned, cream gets separated due to
centripetal force
centrifugal force
fricitional force
gravitational force
An electric fan has blades of length 30 cm measured from the axis of rotation at 120 rev/min, the acceleration of a point on the tip of the blade is
1600 ms-2
47.4 ms-2
23.7 ms-2
50.55 ms-2
Two bodies of same mass are projected with the same velocity at an angle 30° and 60° respectively. The ratio of their horizontal ranges will be
1:1
1:2
1:3
2:√2
The maximum range of a gun of horizontal terrain is 16 km. If g = 10 ms-2,then muzzle velocity of a shell must be
160 ms-1
200√2 ms-1
400 ms-1
800 ms-1
The angle between A and B is θ. The value of the triple product A.(B×A) is
A2B
zero
A2B sinθ
A2B cosθ
A bus is moving on a straight road towards North with a uniform speed of 50 km/h. If the speed remains unchanged after turning through 90°, the increased in the velocity of bus in the turning process is
70.7 km/h along South - West direction
zero
50 km/h along West
70.7 km/h along North - West direction
The magnitudes of vectors A,B and C are 3, 4 and % units respectively. If A+B =C, the angle between a and B is
π/2
cos-1(0.6)
tan-1(7/5)
π/4
