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 |

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Q65:

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 $t( \sqrt 2 + 1 )~s$ . The value of $t$ is:
(Take $g=10$ m/s² )

1. $1$
2. $2$
3. $3$
4. $4$

Subtopic: Uniformly Accelerated Motion |

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Q16:

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 |

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Q134:

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.

If both the assertion and the reason are true and the reason is a correct explanation of the assertion
If both the assertion and reason are true but the reason is not a correct explanation of the assertion
If the assertion is true but the reason is false
If both the assertion and reason are false

Subtopic: Circular Motion |

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Q17:

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: Position & Displacement |

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Q104:

Select the correct option based on the statements given below:

Assertion:	The maximum height of a projectile is always $25$% of the maximum range.
Reason:	For maximum height, the projectile should be projected at $90^\circ.$

1.	Both assertion and reason are correct, reason is the correct explanation of Assertion.
2.	Both assertion and reason are correct but the reason is not the correct explanation of the assertion.
3.	Assertion is correct and the reason is incorrect.
4.	Assertion is incorrect and the reason is correct.

Subtopic: Projectile Motion |

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Q121:

The magnitude of a vector $\vec{A}$ is constant but it is changing its direction continuously. The angle between $\vec{A}$ and $\frac{d \vec{A}}{dt}$ is:

1. 180°

2. 120°

3. 90°

4. 0°

Subtopic: Circular Motion |

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Q30:

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 |

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Q59:

A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) $m / s^{2}$ . What is the speed of the particle at the instant its x-coordinate is 84 m?

1.	36 m/s	2.	26 m/s
3.	1 m/s	4.	0 m/s

Subtopic: Uniformly Accelerated Motion |

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Q63:

A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0ĵ ) $m / s^{2}$ . What is the y-coordinate of the particle at the instant its x-coordinate is 84 m?

1. 36 m

2. 26 m

3. 1 m

4. 0 m

Subtopic: Uniformly Accelerated Motion |

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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. \(r\sqrt{\pi^2+4}\)

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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.	\(42\) m	2.	\(47\) m
3.	\(19\) m	4.	\(40\) m

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. \(r\sqrt{\pi^2+4}\)

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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. \(r\sqrt{\pi^2+4}\)