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 |
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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 cat is situated at point $$A$$ ($$0,3,4$$) and a rat is situated at point $$B$$ ($$5,3,-8$$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. $$5$$ unit
2. $$12$$ unit
3. $$13$$ unit
4. $$17$$ unit

Subtopic:  Position & Displacement |
75%
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A particle is moving on a circular path of radius $$R.$$ When the particle moves from point $$A$$ to $$B$$ (angle $$\theta$$), the ratio of the distance to that of the magnitude of the displacement will be:

 1 $\frac{\mathrm{\theta }}{\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 2 $\frac{\mathrm{\theta }}{2\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 3 $\frac{\mathrm{\theta }}{2\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 4 $\frac{\mathrm{\theta }}{\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 
Subtopic:  Position & Displacement |
75%
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A vector $\stackrel{\to }{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $|\Delta \stackrel{\to }{a}|$ and $\Delta a$ are, respectively:

 1 $$0, ad\theta$$ 2 $$a d\theta, 0$$ 3 $$0,0$$ 4 None of these
Subtopic:  Position & Displacement |
53%
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