# An aeroplane flies $$400$$ m north and then $$300$$ m west and then flies $$1200$$ m upwards. Its net displacement is: 1.  $$1200$$ m 2.  $$1300$$ m 3.  $$1400$$ m 4.  $$1500$$ m

Subtopic:  Position & Displacement |
73%
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Select the incorrect statement:

 1 It is possible to have $$\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| = 0$$ and $$\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}} \neq 0$$ 2 It is possible to have$$\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0$$ and $$\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 .$$ 3 it is possible to have$$\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right|=0$$ and $$\frac{\mathrm{d}|\overrightarrow{\mathrm{v}}|}{\mathrm{dt}}=0 .$$ 4 It is possible to have $$\left|\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}\right| \neq 0$$ $$\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}} \neq 0$$
Subtopic:  Acceleration |
56%
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A particle of mass 2 kg is moving in a circular path with a constant speed of 10 m/s. The change in the magnitude of velocity when a particle travels from P to Q will be: [assume the radius of the circle is 10/${\mathrm{\pi }}^{2}$]

 1 $$10 \sqrt{3}$$ 2 $$20 \sqrt{3}$$ 3 10 4 0
Subtopic:  Circular Motion |
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An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2 m, its velocity is –(4 m/s)$\stackrel{^}{\mathrm{j}}$. What is the object's acceleration when it is at y = 2 m?

1.  $\stackrel{^}{\mathrm{j}}$

2.  $\stackrel{^}{\mathrm{i}}$

3.  $\stackrel{^}{\mathrm{j}}$

4.  $\stackrel{^}{\mathrm{i}}$

Subtopic:  Circular Motion |
52%
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The position of a moving particle at time $$t$$ is $$\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.$$ Its displacement during the time interval $$t=1$$ s to $$t=3$$ s will be:

 1 $$\hat{j}-\hat{k}$$ 2 $$3\hat{i}-4\hat{j}-\hat{k}$$ 3 $$9\hat{i}+36\hat{j}-27\hat{k}$$ 4 $$32\hat{j}-26\hat{k}$$
Subtopic:  Position & Displacement |
80%
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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 |
74%
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A body is projected at an angle of $30°$ with the horizontal with a speed of 30 m/s. What is the angle made by the velocity vector with the horizontal after 1.5 sec? (g = 10$\mathrm{m}/{\mathrm{s}}^{2}$)

1. $0°$

2. $30°$

3. $60°$

4. $90°$

Subtopic:  Projectile Motion |
64%
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A particle moves along the positive branch of the curve $$y= \frac{x^{2}}{2}$$ where $$x= \frac{t^{2}}{2}$$, & $$x$$ and $$y$$ are measured in metres and in seconds respectively. At $$t= 2~\text{s}$$, the velocity of the particle will be:
1. $$\left(\right. 2 \hat{i} - 4 \hat{j})~\text{m/s}$$
2. $$\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right)\text{m/s}$$
3. $$\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) \text{m/s}$$
4. $$\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) \text{m/s}$$

Subtopic:  Speed & Velocity |
73%
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A deer wants to save her life from a lion. The lion follows a path whose equation is ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}=16$. For saving her life, the deer needs to move on a path whose equation will be:

1. ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}=4$

2. ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}=16$

3. ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}-64=0$

4. Both (1) and (3) are correct

Subtopic:  Circular Motion |
64%
From NCERT
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A particle rotates in a circular path starting from rest. If angular acceleration is 4 $rad/{s}^{2}$, then the time after which angle between net acceleration and tangential acceleration becomes $45° is?$

 1 0.5 s 2 0.25 s 3 2 s 4 4 s
Subtopic:  Circular Motion |
50%
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