A boat is sent across a river in a perpendicular direction with a velocity of \(8\ \text{km/hr}\). If the resultant velocity of the boat is \(10\ \text{km/hr}\), then the velocity of the river is:
1. \(10\ \text{km/hr}\)
2. \(8\ \text{km/hr}\)
3. \(6\ \text{km/hr}\)
4. \(4\ \text{km/hr}\)
A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:
| 1. | East-north direction | 2. | West-north direction |
| 3. | South-east direction | 4. | None of these |
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
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 moves with constant angular velocity in a circle. During the motion its:
| 1. | Energy is conserved |
| 2. | Momentum is conserved |
| 3. | Energy and momentum both are conserved |
| 4. | None of the above is conserved |
The angular speed of a flywheel making \(120\ \text{revolutions/minute }\)is:
1. \(2 π\ \text{πππ/π }\)
2. \(4 π^2\ \text{πππ/π }\)
3. \(π\ \text{πππ/π }\)
4. \(4 π\ \text{πππ/π }\)
| 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. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
The angle turned by a body undergoing circular motion depends on time as \(\theta=\theta_0+\theta_1t+\theta_2t^2.\) Then the angular acceleration of the body is:
1. \(\theta_1\)
2. \(\theta_2\)
3. \(2\theta_1\)
4. \(2\theta_2\)
A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb:
1. Falls to earth exactly below the aeroplane
2. Fall to earth behind the aeroplane
3. Falls to earth ahead of the aeroplane
4. Flies with the aeroplane
If a body \(A\) of mass \(M\) is thrown with a velocity \(v\) at an angle of \(30^Β°\) to the horizontal and another body \(B\) of the same mass is thrown with the same speed at an angle of \(60^Β°\) to the horizontal. The ratio of the horizontal range of \(A\) to \(B\) will be:
1. \(1 : 3\)
2. \(1 : 1\)
3. \(1 : \sqrt3\)
4. \( \sqrt3:1\)