Three girls skating on a circular ice ground of radius $$200$$ m start from a point $$P$$ on the edge of the ground and reach a point $$Q$$ diametrically opposite to $$P$$ following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:        1. $$A > B > C$$ 2. $$C > A > B$$ 3. $$B > A > C$$ 4. $$A = B = C$$

Subtopic:  Position & Displacement |
84%
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A stone tied to the end of a string $$80$$ cm long is whirled in a horizontal circle at a constant speed. If the stone makes $$14$$ revolutions in $$25$$ sec, what is the magnitude of the acceleration of the stone?
1. $$8.1$$ ms-2
2. $$7.7$$ ms-2
3. $$8.7$$ ms-2
4. $$9.9$$ ms-2

Subtopic:  Circular Motion |
66%
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Which one of the following is not true?

 1 The net acceleration of a particle in a circular motion is always along the radius of the circle towards the centre. 2 The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point. 3 The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector. 4 None of the above.
Subtopic:  Circular Motion |
58%
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A particle starts from the origin at $$t=0$$ sec with a velocity of $$10\hat j~\text{m/s}$$ and moves in the $$x\text-y$$ plane with a constant acceleration of $$(8.0\hat i +2.0 \hat j)~\text{m/s}^2$$. At what time is the $$x\text-$$coordinate of the particle $$16$$ m?
1. $$2$$ s

2. $$3$$ s

3. $$4$$ s

4. $$1$$ s

Subtopic:  Uniformly Accelerated Motion |
70%
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For any arbitrary motion in space, which of the following relations is true?

 1 $$\overrightarrow{v}_{\text {avg }}=\left(\frac{1}{2}\right)\left[\overrightarrow{v}\left(t_1\right)+\overrightarrow{v}\left(t_2\right)\right]$$ 2 $$\overrightarrow{v}(t)=\overrightarrow{v}(0)+\overrightarrow{a} t$$ 3 $$\overrightarrow{r}({t})=\overrightarrow{r}(0)+\overrightarrow{v}(0){t}+\frac{1}{2} \overrightarrow{a}{t}^2$$ 4 $$\overrightarrow{v}_{\text {avg }}=\frac{\left[\overrightarrow{r}\left(t_2\right)-\overrightarrow{r}\left(t_1\right)\right]}{\left(t_2-t_1\right)}$$

Subtopic:  Speed & Velocity |
62%
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A particle is moving along a circle such that it completes one revolution in $$40$$ seconds. In $$2$$ minutes $$20$$ seconds, the ratio of $$|displacement| \over distance$$ will be:
1. $$0$$
2. $$\frac{1}{7}$$
3. $$\frac{2}{7}$$
4. $$\frac{1}{11}$$

Subtopic:  Position & Displacement |
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Consider the motion of the tip of the second hand of a clock. In one minute (assuming $$R$$ to be the length of the second hand), its:

 1 displacement is $$2\pi R$$ 2 distance covered is $$2R$$ 3 displacement is zero. 4 distance covered is zero.
Subtopic:  Position & Displacement |
86%
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A particle projected from origin moves in the $$x\text-y$$ plane with a velocity $$\overrightarrow{v} = 3 \hat{i} + 6 x \hat{j}$$$\stackrel{}{\mathrm{}}$, where $$\hat i$$ and $$\hat j$$ are the unit vectors along the $$x$$ and $$y\text-$$axis. The equation of path followed by the particle is:
1. $$y=x^2$$
2. $$y=\frac{1}{x^2}$$
3. $$y=2x^2$$
4. $$y=\frac{1}{x}$$

Subtopic:  Speed & Velocity |
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The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by
$$y =4 t - 2 t^{2}~ \text{m}$$ and $$x =3t$$ metre, where $$t$$ is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:
1. $$30^{\circ}$$
2. $$37^{\circ}$$
3. $$45^{\circ}$$
4. $$60^{\circ}$$

Subtopic:  Projectile Motion |
78%
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The velocity at the maximum height of a projectile is $$\frac{\sqrt{3}}{2}$$ times its initial velocity of projection $$(u)$$. Its range on the horizontal plane is:
1. $$\frac{\sqrt{3} u^{2}}{2 g}$$
2. $$\frac{3 u^{2}}{2 g}$$
3. $$\frac{3 u^{2}}{ g}$$
4. $$\frac{u^{2}}{2 g}$$

Subtopic:  Projectile Motion |
73%
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