Q. No.A particle starts from the origin at t=0 and moves in the x-y plane with a constant acceleration 'a' in the y direction. Its equation of motion is . The x component of its velocity (at t=0) will be:
1. variable
2.
3.
4.
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. Width of the river is 1 km. The minimum time taken for a round trip will be
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 of 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 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 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 fly wheel making \(120\) revolutions/minute is:
1. \(2\pi~\mathrm{rad/s}\)
2. \(4\pi^2~\mathrm{rad/s}\)
3. \(\pi~\mathrm{rad/s}\)
4. \(4\pi~\mathrm{rad/s}\)
Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be:
| 1. | \(20 \times 10^8 \mathrm{~m} / \mathrm{s}^2 \) | 2. | \(8 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) |
| 3. | \(120 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) | 4. | \(4 \times 10^8 \mathrm{~m} / \mathrm{s}^2\) |
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
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