A particle is projected at an angle with horizontal with an initital speed u. When it makes an angle with horizontal, its speed v is-
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2.
3.
4.
A particle is moving with veocity ; where k is constant. The general equation for the path is:
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2.
3.
4. xy=constant
A body thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:
1.
2.
3.
4.
A projectile is given an initial velocity of . The cartesian equation of its path is (g = 10 )
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4.
Time taken by the projectile to reach from A to B is t. Then the distance AB is equal to :
1.
2.
3.
4. 2ut
A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr, at an angle with respect to the river. If AB=BC=400m. Then-
(1) time taken by the man is 12 min
(2) time taken by the man is 8 min
(3) the value of is 45
(4) the value of is 53
A body is thrown horizontally with a velocity from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is:
1. | \(\mathrm h \) | 2. | \(\frac{h}{2} \) |
3. | \(2\mathrm h \) | 4. | \( \frac{2 h}{3}\) |
A particle has initial velocity and has acceleration . Its speed after 10 s:
1. 7 units
2. units
3. 8.5 units
4. 10 units
A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is :
(1) 10 km/hr
(2) 8 km/hr
(3) 6 km/hr
(4) 4 km/hr
A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip(returning to the initial point) is:
(1) 5 min
(2) 60 min
(3) 20 min
(4) 30 min
A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south.
(1) 30° with downstream
(2) 60° with downstream
(3) 120° with downstream
(4) South
If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:
1. v2/r
2. vr
3. v/r
4. r/v
Two racing cars of masses \(m_1\) and \(m_2\) are moving in circles of radii \(r_1\) and \(r_2\) respectively. Their speeds are such that each makes a complete circle in the same duration of time \(t\). The ratio of the angular speed of the first to the second car is:
1. \(m_1:m_2\)
2. \(r_1:r_2\)
3. \(1:1\)
4. \(m_1r_1:m_2r_2\)
If a particle moves in a circle describing equal angles in equal times, its velocity vector:
(1) remains constant.
(2) changes in magnitude.
(3) changes in direction.
(4) changes both in magnitude and direction.
A motorcyclist going round in a circular track at a constant speed has:
(1) constant linear velocity.
(2) constant acceleration.
(3) constant angular velocity.
(4) constant force.
A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio
(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 4 : 1
The angular speed of a flywheel making 120 revolutions/minute is:
(1)
(2)
(3)
(4)
Certain neutron stars are believed to be rotating at about 1 rev/sec. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be
(1)
(2)
(3)
(4)
An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m, the acceleration of a point on the tip of the blade is about
(1) 1600 m/sec2
(2) 4740 m/sec2
(3) 2370 m/sec2
(4) 5055 m/sec2
What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\) :
1. | \(6 \hat{i}+2 \hat{j}-3 \hat{k} \) |
2. | \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \) |
3. | \(4 \hat{i}-13 \hat{j}+6 \hat{k}\) |
4. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
If ar and at represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:
1. ar = 0 and at = 0
2. ar = 0 but at \(\neq\) 0
3. ar \(\neq\) 0 but at = 0
4. ar \(\neq\) 0 and at \(\neq\) 0
A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first 2 sec, it rotates through an angle θ1. In the next 2 seconds, it rotates through an additional angle θ2. The ratio of θ2/θ1 is:
1. | 1 | 2. | 2 |
3. | 3 | 4. | 5 |
The coordinates of a moving particle at any time ‘t’ are given by x = αt3 and y = βt3. The speed of the particle at time ‘t’ is given by:
1.
2.
3.
4.
The angle turned by a body undergoing circular motion depends on time as . Then the angular acceleration of the body is
(1) θ1
(2) θ2
(3) 2θ1
(4) 2θ2
An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling
(1) On a parabolic path as seen by pilot in the plane
(2) Vertically along a straight path as seen by an observer on the ground near the target
(3) On a parabolic path as seen by an observer on the ground near the target
(4) On a zig-zag path as seen by pilot in the plane
A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is
(1)
(2)
(3)
(4)
Two bodies are projected with the same velocity. If one is projected at an angle of 30° and the other at an angle of 60° to the horizontal, the ratio of the maximum heights reached is
(1) 3 : 1
(2) 1 : 3
(3) 1 : 2
(4) 2 : 1
A vector \(\vec{a}\) is turned without a change in its length through a small angle \(d\theta\)
1. \(0,\)
2. \(ad\theta,\) \(0\)
3. \(0,\) \(0\)
4. none of these
A steam boat goes across a lake and comes back (a) On a quiet day when the water is still and (b) On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both the days was the same, in which case will the steam boat complete the journey in lesser time:
1. Case (a)
2. Case (b)
3. Same in both case
4. Nothing can be predicted based on given data
To a person, going eastward in a car with a velocity of 25 km/hr, a train appears to move towards north with a velocity of km/hr. The actual velocity of the train will be
(1) 25 km/hr
(2) 50 km/hr
(3) 5 km/hr
(4) km/hr
A bus is moving with a velocity 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus
(1) 50 m/s
(2) 40 m/s
(3) 30 m/s
(4) 20 m/s
The \(x\) and \(y\) coordinates of the particle at any time are \(x = 5t-2t^2\) and \(y=10t\) respectively, where \(x\) and \(y\) are in metres and \(t\) is in seconds. The acceleration of the particle at \(t=2\) s is:
1. \(0\)
2. \(5\) m/s2
3. \(-4\) m/s2
4. \(-8\) m/s2
A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant. Based on the information given, which of the following is true?
1. | Velocity and acceleration, both are parallel to r. |
2. | Velocity is perpendicular to r and acceleration is directed towards the origin. |
3. | Velocity is not perpendicular to r and acceleration is directed away from the origin. |
4. | Velocity and acceleration, both are perpendicular to r. |
A ship A is moving Westwards with a speed of 10 km h-1 and a 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
1., h
2. 5h
3. 5h
4. 10h
If vectors A = cosωt + sinωt and B = (cosωt/2) + (sinωt/2) are functions of time, then the value of t at which they are orthogonal to each other
1. t=/4ω
2. t=/2ω
3. t=/ω
4. t=0
The position vector of a particle as a function of time is given by r = 4sin(2t)+ 4cos(2t) where r is in metre, t is in seconds, and denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
1. Acceleration is along
2. Magnitude of the acceleration vector is v2/R where v is the velocity of the particle
3. Magnitude of the velocity of the particle is 8 m/s
4. 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 m/s and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m/s2) is: [Given, g = 9.8 m/s2]
1. 3.5
2. 5.9
3. 16.3
4. 110.8
A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (vav) from t = 0 to t = 5s is
1. (13+14)
2. (+)
3. 2(+)
4. (+)
The velocity of a projectile at the initial point A is (2i + 3j) m/s. Its velocity (in m/s) at point B is:
1. -2i+3j
2. -2i-3j
3. 2i-3j
4. 2i+3j
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:
1.
2.
3.
4.
A particle has an initial velocity (\(2\mathrm{i}+3\mathrm{j}\)) and an acceleration (\(0.3\mathrm{i}+0.2\mathrm{j}\)). The magnitude of velocity after 10 s will be:
1. \(9 \sqrt{2} ~\text{units} \)
2. \(5 \sqrt{2} ~\text{units} \)
3. \(5 ~\text{units} \)
4. \(9~\text{units} \)
A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 , the range of the missile is:
1. 50 m 2. 60 m
3. 20 m 4. 40 m
A projectile is fired at an angle of 45 with the horizontal. The elevation angle of the projectile at its highest point as seen from the point of projection is:
1. 60 2.
3. 4.
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
1.
2.
3.
4.
A particle moves in the x-y plane according to rule and . The particle follows:
1. | an elliptical path. |
2. | a circular path. |
3. | a parabolic path. |
4. | a straight line path inclined equally to the x and y-axis. |