# The displacement of point $$P$$ on the wheel (see figure) as the wheel completes half revolution while rolling on the ground is:                 1. $$2\pi r$$ 2. $$\pi r$$ 3. $$\pi r+2r$$ 4. $$r\sqrt{\pi^2+4}$$

Subtopic:  Position & Displacement |
73%
From NCERT
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Two inclined planes are placed as shown in the figure. A block is projected from the Point $$A$$ of inclined plane $$AB$$ along its surface with a velocity just sufficient to carry it to the top point $$B$$ at a height of $$10$$ m. After reaching point $$B$$ the block slides down on inclined plane $$BC$$. The time it takes to reach point $$C$$ from point $$A$$ is $$t( \sqrt 2 + 1 )~\text{s}$$. The value of $$t$$ is:
(Take $$g=10$$ m/s2 )

1. $$1$$
2. $$2$$
3. $$3$$
4. $$4$$
Subtopic:  Uniformly Accelerated Motion |
56%
From NCERT
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A person moved from $$A$$ to $$B$$ on a circular path as shown in the figure below. If the distance travelled by him is $$60$$ m, then the magnitude of displacement would be:
(given $$\cos135^\circ =-0.7$$)

1. $$42$$ m
2. $$47$$ m
3. $$19$$ m
4. $$40$$ m
Subtopic:  Position & Displacement |
From NCERT
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Given below are two statements:
 Assertion (A): Uniform circular motion is the only example of a situation in which the speed of a particle remains constant even though a force is acting on the particle. Reason (R): In uniform circular motion, a force acting along the circle pushes the particle forward.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Circular Motion |
From NCERT
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Given below are two statements:
 Assertion (A): For a given initial and final position the average velocity is single-valued while the average speed can have many values. Reason (R): Velocity is a vector quantity and speed is a scalar quantity.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Speed & Velocity |
51%
From NCERT
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Given below are two statements:
 Assertion (A): The maximum height of a projectile is always $$25$$% of the maximum range. Reason (R): For maximum height, the projectile should be projected at $$90^\circ.$$
 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True and (R) is False. 4 (A) is False and (R) is True.
Subtopic:  Projectile Motion |
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The magnitude of vector $$\overrightarrow{A}$$ is constant but it is changing its direction continuously. The angle between $$\overrightarrow{A}$$ and $$\frac{d\overrightarrow{A}}{dt}$$is:
1. $$180^\circ$$
2. $$120^\circ$$
3. $$90^\circ$$
4. $$0^\circ$$

Subtopic:  Circular Motion |
65%
From NCERT
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The following are four different relations about displacement, velocity, and acceleration for the motion of a particle in general. Choose the incorrect statement(s):

 a. $$v_{avg}=\frac{1}{2} [ v(t_{1})+v(t_{2}) ]$$ b. $$v_{avg}=\frac{r(t_{2})-r(t_{1})}{t_{2}-t_{1}}$$ c. $$r=\frac{1}{2}[ v(t_{2})-v(t_{1}) ](t_2-t_1)$$ d. $$a_{avg}=\frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}$$

 1 (a), (d) 2 (a), (c) 3 (b), (c) 4 (a), (b)

Subtopic:  Speed & Velocity |
61%
From NCERT
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A particle starts from the origin at $$t=0$$ with a velocity of $$5.0\hat i$$ m/s and moves in the $$x\text-y$$ plane under the action of a force that produces a constant acceleration of $$(3.0\hat i + 2.0\hat j)~\text{m/s}^2$$. What is the speed of the particle at the instant its $$x\text-$$coordinate is $$84$$ m?

 1 $$36$$ m/s 2 $$26$$ m/s 3 $$1$$ m/s 4 $$0$$ m/s
Subtopic:  Uniformly Accelerated Motion |
70%
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A particle starts from the origin at $$t=0$$ with a velocity of $$5.0\hat i$$ m/s and moves in the $$x\text-y$$ plane under the action of a force that produces a constant acceleration of $$(3.0\hat i + 2.0 \hat j)~\text{m/s}^2$$${}^{}$. What is the y-coordinate of the particle at the instant its $$x\text-$$coordinate is $$84$$ m?
1. $$36$$
2. $$26$$ m
3. $$1$$ m
4. $$0$$ m

Subtopic:  Uniformly Accelerated Motion |
62%
From NCERT
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