Q. No.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
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. | \(30^{\circ}\) with downstream |
| 2. | \(60^{\circ}\) with downstream |
| 3. | \(120^{\circ}\) 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. | \(20 \times 10^8 ~\text{m/s}^2\) | 2. | \(8 \times 10^5 ~\text{m/s}^2\) |
| 3. | \(120 \times 10^5 ~\text{m/s}^2\) | 4. | \(4 \times 10^8 ~\text{m/s}^2\) |
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
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
3. but at = 0
4. and
In \(1.0~\text{s}\), a particle goes from point \(A\) to point \(B\), moving in a semicircle of radius \(1.0~\text{m}\) (see figure). The magnitude of the average velocity is:
| 1. | \(3.14~\text{m/s}\) | 2. | \(2.0~\text{m/s}\) |
| 3. | \(1.0~\text{m/s}\) | 4. | zero |
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