A particle starting from the point \((1,2)\) moves in a straight line in the XY-plane. Its coordinates at a later time are \((2,3).\) The path of the particle makes with x-axis an angle of:
1. | \(30^\circ\) | 2. | \(45^\circ\) |
3. | \(60^\circ\) | 4. | data is insufficient |
A particle is projected from a horizontal plane (x-z plane) such that its velocity vector at time t is given by \(\overrightarrow{\mathrm{v}}=a \hat{i}+(b-c t )\hat{j}.\) Its range on this horizontal plane is given by:
1. | \(\frac{\mathrm{ba}}{\mathrm{c}} \) | 2. | \(\frac{2 \mathrm{ba}}{\mathrm{c}} \) |
3. | \(\frac{3 \mathrm{ba}}{\mathrm{c}} \) | 4. | None |
A river is 1 km wide. The banks are straight and parallel. The current is 5 km/h and is parallel to the banks. A boat has a maximum speed of 3 km/h in still water. In what direction should the boat head so as to arrive at point B directly opposite to its starting point A?
1. directly across the river
2. head upstream from the line AB
3. head
4. the trip from A to B is not possible with this speed
Two particles A and B, move with constant velocities \(\vec{v_1}\) and \(\vec{v_2}\) . At the initial moment their position vector are \(\vec{r_1}\) and \(\vec{r_2}\) respectively. The condition for particles A and B for their collision to happen will be:
1.
2.
3.
4.
A particle moves along a parabolic path y = 9x2 in such a way that the x component of the velocity remains constant and has a value of . It can be deduced that the acceleration of the particle will be:
1.
2.
3.
4.
Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are respectively, then:
1.
2.
3.
4.
Figure below shows a body of mass M moving with a uniform speed v on a circular path of radius, R. What is the change in acceleration in going from P1 to P2?
1. zero
2.
3.
4.
A particle is projected with a speed u at an angle to the horizontal. Radius of curvature at highest point of its trajectory is?
1.
2.
3.
4.
Two particles A and B are moving in a uniform circular motion in concentric circles of radii with speeds respectively. Their time periods of rotation are the same. The ratio of angular speed of A to that of B will be:
1. | \( 1: 1 \) | 2. | \(r_A: r_B \) |
3. | \(v_A: v_B \) | 4. | \(r_B: r_A\) |