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Physics 1 Marks Question

PART - 1 CH - 3 Motion in a Plane · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 44 questions.

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44 questions · timed · auto-graded

Question 11 Mark
Pick out the only vector quantity in the following list :
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
Answer
Impulse = Change in momentum = Force × time
Here both both momentum and force are vector quantities. There force charge will be a vector quantity.
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Question 21 Mark
For any arbitrary motion in space, which of the following relations are true?
(a) $\vec{v}_{\text {avg }}=(1 / 2)\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]$
(b) $\vec{v}_{ avg }=\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right] /\left(t_2-t_1\right)$
(c) $\vec{v}(t)=\vec{v}(0)+\vec{a} t$
(d) $\vec{r}( t )=\vec{r}(0)+\vec{v}(0) t+(1 / 2) \vec{a} t^2$
(e) $\vec{a}_{\text {avg }}=\left[\vec{v}\left(t_2\right)-\vec{v}\left(t_1\right)\right] /\left(t_2-t_1\right)$
Here, 'average' means the average values of physical quantities related to the time interval $t_2$ and $t_1$.
Answer
Relations (b) and (e) are true for any arbitrary motion. Relations (a), (c) and (d) are wrong because they are for uniformly accelerated motion.
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Question 31 Mark
Pick out the two scalar quantities in the following list :
Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
Answer
Work, current.
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Question 41 Mark
State, for each of the following physical quantities, if it is a scalar or a vector : volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
Answer
Scalar quantities : Volume, mass, speed, density, mole number, angular frequency.
Vector quantities : Acceleration, velocity, displacement, angular velocity.
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Question 51 Mark
A ball is thrown in horizontal direction from the top of a tower and another ball is dropped from the top of same tower. What will be the time difference between both the balls to reach the earth?
Answer
Zero. The formula for the vertical motion of both the balls are $s=u t+\frac{1}{2} a t^2$, where $x=0, a=g$. Hence for both the balls $t$ will be same, i.e., both the balls will reach the earth simultaneously.
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Question 61 Mark
What is the position vector of inst. velocity and inst. acceleration of particle moving in a circular path with a constant speed?
Answer
Perpendicular to each other. Since motion at a constant speed in a circular path produces centripetal acceleration, the direction of which is towards the centre
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Question 71 Mark
An ant crawls from its initial position ( $-2 m$, $4 m,-3 m)$ to final position $(6 m,-2 m,-3 m)$. What will be its displacement?
Answer
It is given :
$\begin{array}{l}
\vec{r}_1=-2 \hat{i}+4 \hat{j}-3 \hat{k} \\
\overrightarrow{r_2}=6 \hat{i}-2 \hat{j}-3 \hat{k}
\end{array}$
Displacement,
$\begin{aligned}
\overrightarrow{\Delta r} & =\overrightarrow{r_2}-\overrightarrow{r_1} \\
& =6 \hat{i}-2 \hat{j}-3 \hat{k}+2 \hat{i}-4 \hat{j}+3 \hat{k} \\
\overrightarrow{\Delta r} & =8 \hat{i}-6 \hat{j}
\end{aligned}$
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Question 81 Mark
Write the triangle law of vector addition
Answer
According to this law, if two vectors are represented in the same order in magnitude and direction by two consecutive sides of a triangle, then the third side of triangle represent the resultant vector in opposite direction,
$
\vec{R}=\vec{P}+\vec{Q}
$
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Question 101 Mark
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?
Answer
$y=x \tan \theta \frac{-g x^2}{2 v^2 \cos \theta}$
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Question 111 Mark
When the maximum height obtained by a prejection is the largest, then name the two quantities which will be the largest?
Answer
Time of flight and half component of velocity
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Question 121 Mark
Is circular motion possible at constant speed or constant velocity? Explain
Answer
Circular motion is possible with a constant speed because in this the magnitude of velocity or speed remains constant out the direction of motion of particle keeps changing
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Question 131 Mark
The maximum horizontal range of a projected object is R. What is maximum height it reaches?
Answer
If $\theta=45^{\circ}$ then
$\begin{aligned}
H & =\frac{1}{4}\left(\frac{u^2}{g}\right) \\
R_{\max } & =\frac{u^2}{g} \\
H & =\frac{R_{\max }}{4}
\end{aligned}$
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Question 141 Mark
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?
Answer
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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Question 151 Mark
An object is moving in a plane in a direction different from the direction of its initial velocity. What will be the path covered by it?
Answer
Its path will be a parabolic path
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Question 161 Mark
For the projectile path to be rectilinear, the value of angle of projection should be equal to how many degrees?
Answer
$90^{\circ}$
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Question 171 Mark
At which point in the trajectory will the speed be maximum?
Answer
The point at which the projectile return to the place from where it is lanched.
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Question 191 Mark
At which point in the trajectory of the ball thrown upward the acceleration is perpendicular to velocity?
Answer
At the highest point of projection
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Question 201 Mark
What is meant by horizontal range of projectile? Give example.
Answer
The horizontal distance from the beginning to the end point of flight on the same horizontal plane is called the horizontal range of projectile
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Question 211 Mark
Write the formula of maximum height. What is the velocity of projectile at the maximum height?
Answer
Maximum height $H =\frac{u^2 \sin ^2 \theta}{2 g}$
At the maximum height the velocity of projectile is $u$ $\cos \theta$ only in horizontal direction.
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Question 221 Mark
What do you understand by time of flight?
Answer
It is the time interval in which the projectile returns to its initial horizontal plane after being thrown. This time is equal to the vertical upward time of any body. Hence if the time of flight is T then
$
T=\frac{2 u \sin \theta}{g}
$
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Question 231 Mark
What will be the angle formed between the directions of velocity and acceleration of the particle at the highest point of the path?
Answer
$90^{\circ}$
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Question 241 Mark
At what inclination should a player throw the ball from horizontal so that the ball travels the maximum distance?
Answer
$45^{\circ}$
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Question 251 Mark
At which points of trajectory speed will be minimum and maximum?
Answer
At the highest point, at the projection point.
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Question 261 Mark
What is the angle between the direction of velocity and acceleration at the highest point of trajectory?
Answer
$90^{\circ}$
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Question 271 Mark
Why does the direction of motion of the projectile becomes horizontal at the highest point of trajectory?
Answer
Because the vertical velocity becomes zero at the highest point
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Question 281 Mark
A football player throws the ball at an angle of $30^{\circ}$ to the horizontal with velocity $50 m / s$. Find out the maximum height attained by ball?
Answer
$\begin{array}{l}
\text { Maximum height } H=\frac{u^2 \sin ^2 \theta}{2 g} \\
\qquad H=\frac{50 \times 50 \times \frac{1}{2} \times \frac{1}{2}}{2 \times 10}=31.25 m
\end{array}$
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Question 291 Mark
Why does a cyclist bends towards the center of turn from the vertical while taking a circular turn?
Answer
To provide centripetal force
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Question 301 Mark
If $\vec{A}-\vec{B}=\vec{A}+\vec{B}$, then the value of $\vec{B}$ will
Answer
 $ \vec{A}-\vec{B}=\vec{A}+\vec{B}$
$2 \vec{B}=0$
or
$\overrightarrow{B}=0$
Hence, the above equation will be true only when $\vec{B}$ is a zero vector.
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Question 311 Mark
Which components remains constant in the instantaneous velocity components $v_x, v_y$ and in acceleration components $a_x, a_y$ of a projectile?
Answer
In a projectile motion, the horizontal component of velocity $v_x$ remains constant while the vertical component of velocity $v_y$ changes due to acceleration due to gravity.
$
v_x=u \cos \theta, a_x=0 \text { and } a_y=-g
$
$\therefore v_x, a_y, a_y$ will remain constant
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Question 331 Mark
When the projectile is moving at an angle $\theta$, then what can be the maximum and minimum angle in instantaneous velocity and instantaneous acceleration?
Answer
$\frac{\pi}{2}+\theta, \frac{\pi}{2}-\theta$.
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Question 341 Mark
Are physical quantities having both magnitude and direction always vector quantities?
Answer
No. They are vector quantities if they obey the law of vector addition, i.e., $\overrightarrow{ A }+\overrightarrow{ B }=\overrightarrow{ B }+\overrightarrow{ A }$. For example, electric current, time etc. are scalar even while keeping the direction.
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Question 351 Mark
$I ^{\text {st }}$ it possible that the sum and difference of two vectors be in same direction? If yes, then under what circumstances?
Answer
Yes, it is possible. This will be possible when both the vectors are unequal in magnitude but equal in direction.
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Question 361 Mark
If $\vec{A} \cdot \vec{B}=\vec{A} \cdot \vec{C}$, then should $\vec{B}$ and $\vec{C}$ be equal?
Answer
Generally not, but if angle between $\vec{A}$ and $\vec{B}$ is equal to angle between $\vec{A}$ and $\vec{C}$ then $\vec{B}=\vec{C}$
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Question 371 Mark
Can the value of resultant vector of two vectors be less than the value of any one of the given vectors?
Answer
Yes, if the angle between the vectors is more than $90^{\circ}$.
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Question 381 Mark
If one component of a vector is zero, and other component is not zero then can that vector be zero?
Answer
No
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Question 391 Mark
Can a scalar and a vector quantity be added?
Answer
No. Scalar quantity doesn't have direction while vector quantity has direction. Therefore, there is a difference in the algebra of addition
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Question 401 Mark
If a vector $\vec{A}$ is multiplied by a scalar $m$, what will be the resulting vector?
Answer
$m \vec{A}$
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Question 411 Mark
Can three vector quantities can be added in such a way that their resultant vector is zero?
Answer
Yes, when their magnitude and direction are represented as the three sides of a triangle in a sequence
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Question 421 Mark
When is sum of two vectors always maximum and when is it minimum?
Answer
When both vectors are in same direction when both vectors are in opposite direction
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