A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be 1. 5  m 2. 4.8 m 3. 3.2 m 4. 3.0 m

Subtopic:  Relative Motion |
51%
From NCERT
PMT - 2002
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A particle is projected at an angle $\theta$ with horizontal with an initital speed u. When it makes an angle $\alpha$ with horizontal, its speed v is-

1. $u\mathrm{cos}\theta$

2.

3. $\frac{u\mathrm{sin}\theta }{\mathrm{sin}\alpha }$

4. $\frac{u\mathrm{cos}\theta }{\mathrm{cos}\alpha }$

Subtopic:  Projectile Motion |
From NCERT
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A particle is moving along the path y = ${\mathrm{x}}^{2}$ from x = 0 m to x = 2 m. Then the distance traveled by the particle is:

1.  4 m

2.

3.

4.

Subtopic:  Position & Displacement |
From NCERT
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Six particles situated at the corners of a regular hexagon of side $$a$$ move at constant speed $$v$$. Each particle maintains a direction towards the particle at the next. The time which the particles will take to meet each other is:
1. $$\frac{2 a}{v}~\text{sec}$$
2. $$\frac{a}{v}~\text{sec}$$
3. $$\frac{2 a}{3v}~\text{sec}$$
4. $$\frac{3 a}{v}~\text{sec}$$

Subtopic:  Relative Motion |
From NCERT
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A body is projected with velocity $20\sqrt{3}$ m/s with an angle of projection 60$°$ with horizontal. Calculate velocity on that point where body makes an angle 30$°$ with the horizontal.

1. 20 m/s

2.

3.

4. 10 m/s

Subtopic:  Projectile Motion |
65%
From NCERT
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In a uniform circular motion, which of the following quantity is not constant

1. Angular momentum

2. Speed

3. Kinetic energy

4. Momentum

Subtopic:  Circular Motion |
52%
From NCERT
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A particle is moving with veocity $\stackrel{\to }{\mathrm{v}}=\mathrm{k}\left(\mathrm{y}\stackrel{^}{\mathrm{i}}+\mathrm{x}\stackrel{^}{\mathrm{j}}\right)$; where k is constant. The general equation for the path is:

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

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

3. $\mathrm{y}=\mathrm{x}+\mathrm{constant}$

4. xy=constant

Subtopic:  Speed & Velocity |
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A particle is projected with a velocity u making an angle $\mathrm{\theta }$ with the horizontal. At any instant, its velocity v is at right angles to its initial velocity u; then v is:

1.  ucos$\mathrm{\theta }$

2.  utan$\mathrm{\theta }$

3.  ucot$\mathrm{\theta }$

4.  usec$\mathrm{\theta }$

Subtopic:  Projectile Motion |
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A projectile is given an initial velocity of $\stackrel{^}{i}+2\stackrel{^}{j}$. The cartesian equation of its path is (g = 10 ${\mathrm{ms}}^{-2}$

1. $\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^{2}$

2. $\mathrm{y}=\mathrm{x}-5{\mathrm{x}}^{2}$

3. $4\mathrm{y}=2\mathrm{x}-5{\mathrm{x}}^{2}$

4. $\mathrm{y}=2\mathrm{x}-25{\mathrm{x}}^{2}$

Subtopic:  Projectile Motion |
58%
From NCERT
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A ship A is moving westwards with a speed of 10 km ${\mathrm{h}}^{-1}$ and a ship B, 100 km south of A is moving northwards with a speed of 10 km ${\mathrm{h}}^{-1}$. The time after which the distance between them becomes the shortest, is:

1. 5 hr

2. $5\sqrt{2}$ hr

3. $10\sqrt{2}$ hr

4. 0 hr

Subtopic:  Relative Motion |
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