# Two particles $$A$$ and $$B$$ are moving in a uniform circular motion in concentric circles of radii $$r_A$$ and $$r_B$$ with speeds $$v_A$$ and $$v_B$$ respectively. Their time periods of rotation are the same. The ratio of the angular speed of $$A$$ to that of $$B$$ will be: 1. $$1: 1$$ 2. $$r_A: r_B$$ 3. $$v_A: v_B$$ 4. $$r_B: r_A$$

Subtopic:  Circular Motion |
79%
From NCERT
NEET - 2019
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A particle is projected with a speed $$u$$ at an angle $$\theta$$ to the horizontal. Radius of curvature at highest point of its trajectory is?
1. $$\frac{u^{2} \cos^{2} \theta}{2 g}$$
2. $$\frac{\sqrt{3} u^{2}\cos^{2} \theta}{2 g}$$
3. $$\frac{u^{2} \cos^{2} \theta}{g}$$
4. $$\frac{\sqrt{3} u^{2} \cos^{2} \theta}{g}$$

Subtopic:  Circular Motion |
From NCERT
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Figure below shows a body of mass $$M$$ moving with a uniform speed $$v$$ on a circular path of radius, $$R$$. What is the change in acceleration in going from $$P_1$$ to $$P_2$$

1. zero
2. $$v^{2} / 2 R$$
3. $$2 v^{2} / R$$
4. $$\frac{v^{2}}{R} \times \sqrt{2}$$

Subtopic:  Circular Motion |
From NCERT
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Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are $$v_{1} , v_{2}$$ $$\text{and}$$ $$v_{3}$$ respectively, then:

1. $$v_{1} > v_{2} > v_{3}$$
2. $$v_{3} > v_{2} = v_{1}$$
3. $$v_{1} = v_{2} = v_{3}$$
4. $$v_{1} < v_{2} < v_{3}$$${}_{}$

Subtopic:  Projectile Motion |
74%
From NCERT
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A particle moves along a parabolic path $$y =9x^2$$ in such a way that the $$x$$ component of the velocity remains constant and has a value of $$\frac{1}{3}~\text{m/s}$$${}^{}$. It can be deduced that the acceleration of the particle will be:
1. $$\frac{1}{3}\hat j~\text{m/s}^2$$
2. $$3\hat j~\text{m/s}^2$$
3. $$\frac{2}{3}\hat j~\text{m/s}^2$$
4. $$2\hat j~\text{m/s}^2$$

Subtopic:  Acceleration |
From NCERT
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Two particles $$A$$ and $$B$$, move with constant velocities $$\overrightarrow{v_1}$$ and $$\overrightarrow{v_2}$$. At the initial moment their position vector are $$\overrightarrow {r_1}$$ and $$\overrightarrow {r_2}$$ respectively. The condition for particles $$A$$ and $$B$$ for their collision to happen will be:

 1 $$\overrightarrow{r_{1 }} . \overrightarrow{v_{1}} = \overrightarrow{r_{2 }} . \overrightarrow{v_{2}}$$ 2 $$\overrightarrow{r_{1}} \times\overrightarrow{v_{1}} = \overrightarrow{r_{2}} \times \overrightarrow {v_{2}}$$ 3 $$\overrightarrow{r_{1}}-\overrightarrow{r_{2}}=\overrightarrow{v_{1}} - \overrightarrow{v_{2}}$$ 4 $$\frac{\overrightarrow{r_{1}} - \overrightarrow{r_{2}}}{\left|\overrightarrow{r_{1}} - \overrightarrow{r_{2}}\right|} = \frac{\overrightarrow{v_{2}} - \overrightarrow{v_{1}}}{\left|\overrightarrow{v_{2}} - \overrightarrow{v_{1}}\right|}$$
Subtopic:  Speed & Velocity |
71%
From NCERT
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A particle starting from the point $$(1,2)$$ moves in a straight line in the XY-plane. Its coordinates at a later time are $$(2,3).$$ The path of the particle makes with $$x$$-axis an angle of:

 1 $$30^\circ$$ 2 $$45^\circ$$ 3 $$60^\circ$$ 4 data is insufficient
Subtopic:  Position & Displacement |
81%
From NCERT
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A car turns at a constant speed on a circular track of radius $$100$$ m, taking $$62.8$$ s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

 1 $$0,~0$$ 2 $$0,~10$$ m/s 3 $$10$$ m/s, $$10$$ m/s 4 $$10$$ m/s, $$0$$
Subtopic:  Speed & Velocity |
82%
From NCERT
AIPMT - 2006
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For a projectile projected at angles $$(45^{\circ}-\theta)$$ and $$(45^{\circ}+\theta)$$, the horizontal ranges described by the projectile are in the ratio of:
1. $$1:1$$
2. $$2:3$$
3. $$1:2$$
4. $$2:1$$

Subtopic:  Projectile Motion |
87%
From NCERT
AIPMT - 2006
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A particle starting from the origin $$(0,0)$$ moves in a straight line in the $$(x,y)$$ plane. Its coordinates at a later time are ($\sqrt{3}$, $$3).$$ The path of the particle makes an angle of __________ with the $$x$$-axis:
1. $$30^\circ$$
2. $$45^\circ$$
3. $$60^\circ$$
4. $$0$$

Subtopic:  Position & Displacement |
76%
From NCERT
AIPMT - 2007
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