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Q. No.The horizontal range of a projectile fired at an angle of \(15^\circ\) is \(50\) m. If it is fired with the same speed at an angle of \(45^\circ\), its range will be:
1. \(60\) m
2. \(71\) m
3. \(100\) m
4. \(141\) 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. | average acceleration must always vanish. |
| 3. | 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 alternative/s is/are:
| 1. | (a), (d) | 2. | (a), (c) |
| 3. | (b), (c) | 4. | (a), (b) |
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)
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Q. No.
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