A car moves on a circular path such that its speed is given by v = Kt, where K =constant and t is time. Also given: radius of the circular path is r. The net acceleration of the car at time t will be:
1.
2. 2K
3. K
4.
Raindrops are falling with a speed v vertically downwards and a man is running on a horizontal road with speed u. The magnitude of the velocity of the raindrops with respect to the man is:
1. v - u
2. v + u
3. \(\sqrt{\text{v}^2 + \text{u}^2 \over 2}\)
4. \(\sqrt{\text{v}^2 + \text{u}^2}\)
A boy runs on a circular track of radius \(\mathrm{R}\) (in km) with a speed of km/h in the clockwise direction for \(3\) h and then with km/h in the anticlockwise direction for \(1\) h. The magnitude of his displacement will be:
1.
2.
3.
4.
The equation of trajectory of a projectile is given by y = x - 10. Its speed of projection is: (g = 10 m/)
1. 1 m/s
2. 2 m/s
3. 3 m/s
4. 4 m/s
A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by . The equation of the trajectory of the body is:
1. y = 1.5 x
2. y = 0.75
3. y = 1.5
4. y = 0.45
A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m
If a particle is moving in a circular orbit with constant speed, then:
1. | its velocity is variable. |
2. | its acceleration is variable. |
3. | its angular momentum is constant. |
4. | All of the above |
A projectile is projected with initial kinetic energy K. If it has kinetic energy 0.25K at its highest point, then the angle of projection is:
1. 30°
2. 45°
3. 60°
4. 75°
If the position of a particle varies according to the equations \(x= 3t^2\), \(y =2t\), and \(z= 4t+4\), then which of the following is incorrect?
1. | Velocities in \(y\) and \(z\) directions are constant |
2. | Acceleration in the \(x\text-\)direction is non-uniform |
3. | Acceleration in the \(x\text-\)direction is uniform |
4. | Motion is not in a straight line |
If three coordinates of a particle change according to the equations , then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. | unit | 2. | unit |
3. | \(40\) unit | 4. | unit |