Question types

PART - 1 CH - 3 Motion in a Plane question types

108 questions across 8 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

108
Questions
8
Question groups
5
Question types
Sample Questions

PART - 1 CH - 3 Motion in a Plane questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

In uniform circular motion
  • Both velocity and acceleration change
  • B
    Both velocity and acceleration are constant
  • C
    Velocity remains constant and acceleration changes
  • D
    Acceleration remains constant and velocity changes.

Answer: A.

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The speed at the maximum height of a projectile is half of its initial speed $u$. The horizontal range of projectile is
  • A
    $\frac{3 u^2}{2 g}$
  • B
    $\frac{\sqrt{3} u^2}{2 g}$
  • C
    $\frac{u^2}{2 g}$
  • D
    $\frac{2 u^2}{g}$
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Two particles of equal masses are moving with equal speed on circular paths of radii $r_1$ and $r_2$. The ratio of their centripetal forces will be
  • $\frac{r_2}{l_1}$
  • B
    $\frac{r_1}{r_2}$
  • C
    $\left(\frac{r_2}{r_1}\right)^2$
  • D
    $\left(\frac{r_1}{r_2}\right)^2$

Answer: A.

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A ball is fired at a vertical hill at a distance $x$ from a cannon aimed at an angle $\theta$ above the horizontal on plane with a nozzle speed $v$. At what height $y$ of the hill from the bottom will the sphere hit?
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A ball is thrown from the top of a tower with a velocity u in the horizontal direction and other ball is drapped from the same place. Will both have the same velocity when they collide with the earth?
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A 0.1 kg stone tied to a thread of 1 m long and moves in a horizontal circular path at a speed of 2 rotations per second. Calculate the tension on the thread.
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Two bodies are thrown from the same point with the same velocity at two different angles. Range is same as $R$ for both the bodies and time of flight is $t$ and $t^{\prime}$ then prove that
$R=\frac{1}{2} g t t^{\prime}$
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From a 20 m high tower, a bullet is fired from a gun in the horizontal direct. If $g=10 ms^{-2}$, and initial velocity of bullet is $400 ms^{-1}$ then at what distance will be bullet fall on the earth?
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A ball is thrown with a velocity of $15 ms^{-1}$ at angle $45^{\circ}$ with the horizontal. What is the range of ball? What is the time of flight for the ball to return to same plane from the point of throwing?
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Prove that when there is an angle $\frac{2}{3} \pi$ between two vectors of equal magnitude, then the magnitude of resultant vector will be equal to the magnitude of one of the vectors.
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Q 223 Marks Question3 Marks
The horizontal range of cannon ball is $R$. If the greatest heights of two paths, for which this is possible, are $h$ and $h ^{\prime}$ then prove that
$4 \sqrt{h h^{\prime}}=R$
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Q 233 Marks Question3 Marks
A player can throw a stone to a maximum horizontal distance of 100 m . What is the maximum vertical height to which the player can throw the same stone?
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Q 243 Marks Question3 Marks
The position vector of a particle depends on time as follows (in meters).
$\vec{r}=\left(2+3 t-t^3\right) \hat{i}+\left(-t+t^2\right) \hat{j}+\left(7 t+t^3\right) \hat{k}$
Find (i) Displacement of particle from $t=0 sec$ to $t=1 sec$ (ii) At $t=1 sec$, find the magnitude of instantaneous velocity and instantaneous acceleration of particle.
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Q 253 Marks Question3 Marks
The resultant of two vector $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If the direction of $\vec{Q}$ is reversed, then the resulting vector becomes $\vec{S}$. Then prove that,
$
R ^2+ S ^2=2\left( P ^2+ Q ^2\right)
$
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Two vector forces 5 N and 3 N are acting on a particle. Find the magnitude and direction of resultant force.(a) When both the forces are in same direction.(b) When both the forces are at right angles.(c) When both the forces are inclined at angle $60^{\circ}$.
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Derive the formula for centripetal acceleration of a particle moving with constant speed on a plane circular path. Or Derive the formula of acceleration for a particle moving with uniform speed on a circular path and tell its direction.
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Prove that the path of projectile thrown at an angle $\theta$ to the horizontal plane will be parabolic. Obtain the formula for the maximum height attained by this.
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What is projectile motion? Drive formula for time of flight and range of projectile fired from a point at an angle $\theta$ with the horizontal. Find value of $\theta$ for maximum horizontal range.
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Column - AColumn - B
1. The value of centripetal acceleration (A) $|\overrightarrow{ A }|=$
2. $\overrightarrow{A}=A_x \hat{i}+A_y \hat{j}+A_z \hat{k}$
the magnitude of $|\overrightarrow{ A }|$ will be :
(B) $H _{\max }=\frac{1}{4} R _{\max }$
3. Instantaneous acceleration
$\vec{a}=$
(C) Tangential
4. What is the relationship between maximum height and maximum range.(D) $\frac{d v}{d t}$
5. The velocity vector is always in the path of motion(E) $\frac{ V ^2}{ R }$
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Column - AColumn - B
1. Position vector of a particle located at point $P$ is
$\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$
the resultant of this $|\vec{r}|=$
(A) $45^{\circ}$
2. A vector can be expressed as the product of its magnitude and unit vectorthen $\vec{A}=$(B) $\sqrt{x^2+y^2+z^2}$
3. When $\vec{P}$ and $\vec{Q}$ are in opposite directions then magnitude of $\vec{R} \ldots$.(C) 1
4. The sum of squares of all three direction cosines of a vector is always,(D) $\hat{n}|\overrightarrow{A}|$
5. The value of $\theta$ for maximum range in $R =\frac{u^2 \sin 2 \theta}{g}$ should be(E) Minimum
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