Q. No.A person is sitting in a traveling train and facing the engine. He tosses up a coin and the coin falls behind him. It can be concluded that the train is:
1. Moving forward and gaining speed.
2. Moving forward and losing speed.
3. Moving forward with uniform speed.
4. Moving backward with uniform speed.
For a particle performing uniform circular motion, choose the correct statement(s) from the following:
1. Magnitude of particle velocity (speed) remains variable.
2. Particle velocity remains directed parallel to radius vector.
3. Direction of acceleration keeps changing as particle moves.
4. Angular momentum is constant in magnitude but direction keeps changing.
The horizontal range of a projectile fired at an angle of 15o is 50 m. If it is fired with the same speed at an angle of 45o, its range will be:
1. 60 m
2. 71 m
3. 100 m
4. 141 m
Three particles A, B, and C are projected from the same point with same initial speeds making angles 30o, 45o, and 60o, respectively, with the horizontal. Which of the following statements is correct?
1. A and C do not have equal ranges.
2. Ranges of A and C are equal and less than that of B.
3. Ranges of A and C are equal and greater than that of B.
4. A, B and C have equal ranges.
The horizontal range of a projectile fired at an angle of \(15^\circ\) is \(50~\text m.\) If it is fired with the same speed at an angle of \(45^\circ,\) its range will be:
1. \(60~\text m\)
2. \(71~\text m\)
3. \(100~\text m\)
4. \(141~\text m\)
In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | The average velocity is not zero at any time. |
| 2. | The average acceleration must always vanish. |
| 3. | The displacements in equal time intervals are equal. |
| 4. | Equal path lengths are traversed in equal intervals. |
In a two-dimensional motion, the instantaneous speed of a particle remains constant at a positive value \(v_0.\) Which of the following statements must always be true?
| 1. | The particle has zero acceleration. |
| 2. | The particle’s acceleration is increasing. |
| 3. | The particle’s acceleration always lies in the plane of motion. |
| 4. | The particle necessarily moves in a uniform circular path. |
A particle slides down a frictionless parabolic track starting from rest at point \(A\). Point \(B\) is at the vertex of the parabola and point \(C\) is at a height less than that of point \(A\). After \(C\), the particle moves freely in the air as a projectile. If the particle reaches the highest point at \(P\), then,
| 1. | kinetic energy at \(P\) = kinetic energy at \(B\) |
| 2. | height at \(P\) = height at \(A\) |
| 3. | total energy at \(P\) = total energy at \(A\) |
| 4. | time of travel from \(A\) to \(B\) = time of travel from \(B\) to \(P\) |
The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.
| (a) | \(v_{a v}=1 / 2\left[v\left(t_1\right)+v\left(t_2\right)\right]\) |
| (b) | \(v_{{av}}={r}\left({t}_2\right)-{r}\left({t}_1\right) / {t}_2-{t}_1\) |
| (c) | \(r=1 / 2\left[v\left(t_2\right)-v\left(t_1\right)\right]\left({t}_2-{t}_1\right)\) |
| (d) | \({a}_{{av}}=v\left({t}_2\right)-v\left({t}_1\right) / {t}_2-{t}_1\) |
The incorrect options is/are:
| 1. | (a) and (d) only | 2. | (a) and (c) only |
| 3. | (b) and (c) only | 4. | (a) and (b) only |
For a particle performing uniform circular motion,
| (a) | the magnitude of particle velocity (speed) remains constant. |
| (b) | particle velocity is always perpendicular to the radius vector. |
| (c) | the direction of acceleration keeps changing as the particle moves. |
| (d) | angular momentum is constant in magnitude but direction keeps changing. |
Choose the correct statement/s:
| 1. | (c), (d) | 2. | (a), (c) |
| 3. | (b), (c) | 4. | (a), (b), (c) |
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