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Q. No.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, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | The acceleration of the particle is zero. |
| 2. | The acceleration of the particle is increasing. |
| 3. | The acceleration of the particle is necessarily in the plane of motion. |
| 4. | The particle must be undergoing a uniform circular motion. |
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) |
Two particles are projected in the air with speed \(v_0\), at angles \(\theta_1\) and \(\theta_2\) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then:
| (a) | the angle of the projection: \(\theta_1>\theta_2\) |
| (b) | the time of flight: \(T_1>T_2\) |
| (c) | the horizontal range: \(R_1>R_2\) |
| (d) | the total energy: \(U_1>U_2\) |
Choose the correct option:
1. (a), (c), (d)
2. (a), (c)
3. (b), (c), (d)
4. (a), (b)
a. the direction of motion of the ball changes every 10 seconds.
b. speed of the ball changes every 10 seconds.
c. average speed of the ball over any 20 second interval is fixed.
d. the acceleration of ball is the same as from the train
Choose the correct option:
1. (a), (d)
2. (b), (c), (d)
3. (a), (b), (c)
4. (b), (c)
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Q. No.
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