# 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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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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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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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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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 $$\mathrm{ABCDEF}$$ 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
Hints

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)
Subtopic:  Circular Motion |
74%
From NCERT
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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.
Subtopic:  Speed & Velocity |
50%
From NCERT
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