1. | The velocity and acceleration both are parallel to \(\vec{r }.\) |
2. | The velocity is perpendicular to \(\vec{r }\) and acceleration is directed towards to origin. |
3. | The velocity is parallel to \(\vec{r }\) and acceleration is directed away from the origin. |
4. | The velocity and acceleration both are perpendicular to \(\vec{r}.\) |
Two particles \({A}\) and \({B}\), move with constant velocities \(\vec{v}_1\) and \(\vec{v}_2\) respectively. At the initial moment, their position vectors are \(\vec{r}_1\) and \(\vec r_2\) respectively. The conditions for particles \({A}\) and \({B}\) for their collision will be:
1. | \(\dfrac{\vec{r}_1-\vec{r}_2}{\left|\vec{r}_1-\vec{r}_2\right|}=\dfrac{\vec{v}_2-\vec{v}_1}{\left|\vec{v}_2-\vec{v}_1\right|}\) |
2. | \(\vec{r}_1 \cdot \vec{v}_1=\vec{r}_2 \cdot \vec{v}_2\) |
3. | \(\vec{r}_1 \times \vec{v}_1=\vec{r}_2 \times \vec{v}_2\) |
4. | \(\vec{r}_1-\vec{r}_2=\vec{v}_1-\vec{v}_2\) |
1. | Acceleration is along \((\text{-}\vec R )\). |
2. | Magnitude of the acceleration vector is \(\frac{v^2}{R}\), where \(v\) is the velocity of the particle. |
3. | Magnitude of the velocity of the particle is \(8\) m/s. |
4. | Path of the particle is a circle of radius \(4\) m. |
The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |
3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |
A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:
1. | \(25\) m/s2 | 2. | \(36\) m/s2 |
3. | \(5\) m/s2 | 4. | \(15\) m/s2 |
A missile is fired for a maximum range with an initial velocity of \(20~\text {m/s}.\) If \(g=10~\text{m/s}^2,\) then the range of the missile will be:
1. | \(50~\text m\) | 2. | \(60~\text m\) |
3. | \(20~\text m\) | 4. | \(40~\text m\) |
A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:
1.
2.
3.
4. zero
A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are (, \(3).\) The path of the particle makes an angle of __________ with the \(x\)-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)
For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)