# Let $$\mathrm{ABCDEF}$$ be a regular hexagon, with the vertices taken in order. The resultant of the vectors: $$\overrightarrow{AB},~\overrightarrow{BC},~\overrightarrow{CD},~\overrightarrow{DE}$$ equals, in magnitude, the vector: 1. $$\overrightarrow{AB}$$  2. $$\overrightarrow{AD}$$ 3. $$\sqrt2\overrightarrow{AB}$$  4. $$\sqrt3\overrightarrow{AB}$$

Subtopic:  Resultant of Vectors |
From NCERT
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Two projectiles are launched, one at twice the speed of the other; the slower one at $$30^\circ$$ and the faster one at $$60^\circ.$$ Their horizontal ranges are in the ratio: (slower : faster)

 1 $$\dfrac{1}{2}$$ 2 $$\dfrac{1}{4}$$ 3 $$\dfrac{1}{6}$$ 4 $$\dfrac{1}{12}$$
Subtopic:  Projectile Motion |
77%
From NCERT
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In a projectile motion the velocity,

 1 is always perpendicular to the acceleration 2 is never perpendicular to the acceleration 3 is perpendicular to the acceleration for one instant only 4 is perpendicular to the acceleration for two instants
Subtopic:  Projectile Motion |
63%
From NCERT
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Let $$\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},$$ then:

 1 $$|\overrightarrow{\mathrm{C}}|$$ is always greater than $$|\overrightarrow{\mathrm{A}}|$$ 2 It is possible to have $$|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{A}}|$$ and $$|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{B}}|$$ 3 $$|\overrightarrow{\mathrm{C}}|$$ is always equal to $$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|$$ 4 $$|\overrightarrow{\mathrm{C}}|$$ is never equal to $$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|$$
Subtopic:  Resultant of Vectors |
57%
From NCERT
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Consider the two situations shown in the figures. In figure (A), the particle $$P$$ is given a velocity $$u$$ up a smooth horizontal incline and it reaches a maximum vertical height $$h_A$$. In figure (B), the same particle $$P$$ is projected with a velocity $$u$$ at an angle $$\theta$$ (parallel to the previous incline) and reaches a maximum height $$h_B$$.
Then,
 1 $$h_A=h_B~\text{sin}\theta$$ 2 $$h_A~\text{sin}\theta=h_B$$ 3 $$h_A~\text{sin}^2\theta=h_B$$ 4 $$\frac{h_A}{\text{sin}^2\theta}=h_B$$
Subtopic:  Projectile Motion |
54%
From NCERT
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A projectile is fired so as to give a maximum horizontal range of $$1$$ km. What would be the maximum height reached by it if it were to be fired vertically upward?
 1 $$2$$ km 2 $$1$$ km 3 $$\dfrac12$$ km 4 $$\dfrac14$$ km
Subtopic:  Projectile Motion |
55%
From NCERT
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An insect trapped in a circular groove of radius $$12$$ cm moves along the groove steadily and completes $$7$$ revolutions in $$100$$ s. What is the angular speed of the motion?

 1 $$0.62$$ rad/s 2 $$0.06$$ rad/s 3 $$4.40$$ rad/s 4 $$0.44$$ rad/s
Subtopic:  Circular Motion |
70%
From NCERT
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The position of a particle is given by;
$$\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})$$ m where $$t$$ is in seconds and the coefficients have the proper units for $$r$$ to be in metres. The magnitude and direction of $$\vec{v}(t)$$ at$$t=1.0$$ s are:
1. $$4$$m/s,$$53^\circ$$ with $$x$$-axis
2. $$4$$ m/s, $$37^\circ$$ with $$x$$-axis
3. $$5$$ m/s,$$53^\circ$$ with $$y$$-axis
4. $$5$$m/s, $$53^\circ$$ with $$x$$-axis
Subtopic:  Speed & Velocity |
68%
From NCERT
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Two particles having mass $$M$$ and $$m$$ are moving in a circular path having radius $$R$$ & $$r$$ respectively. If their time periods are the same, then the ratio of angular velocities will be:
1. $$\frac{r}{R}$$
2. $$\frac{R}{r}$$
3. $$1$$
4. $$\sqrt{\frac{R}{r}}$$

Subtopic:  Circular Motion |
78%
From NCERT
AIPMT - 2001
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If two projectiles, with the same masses and with the same velocities, are thrown at an angle $$60^\circ$$ & $$30^\circ$$ with the horizontal, then which of the following quantities will remain the same?

 1 time of flight 2 horizontal range of projectile 3 maximum height acquired 4 all of the above

Subtopic:  Projectile Motion |
79%
From NCERT
AIPMT - 2000
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